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International audience; Most recent methods of image augmentation and prediction are building upon the deep learning paradigm. A careful preparation of the image dataset and the choice of a suitable network architecture are crucial steps to assess the desired image features and, thence, achieve accurate predictions. We first propose to help the learning process by adding structural information with specific distance transform to the input image data. To handle cases with limited number of training samples, we propose a patch-based procedure with a stratified sampling method at inference. We validate our approaches on two image datasets, corresponding to two different tasks. The ability of our method to segment and predict images is investigated through the ISBI 2012 segmentation challenge dataset and generated electric field masks, respectively. The obtained results are evaluated using appropriate metrics: VRand for image segmentation and SSIM, UIQ and PSNR for image prediction. The proposed techniques demonstrate that the established framework is a reliable estimation method that could be used for a wide range of applications.

Cutter-workpiece engagement (CWE) is fundamental to the process mechanics and dynamics modeling. Due to the variation of the feed directions in five-axis milling of freeform surfaces, the instantaneous CWE is complex and time-varying. Therefore, for the industrial part milling process which contains tremendous cutter locations, how to calculate the CWE efficiently and accurately remains a challenge. In this paper, a high efficiency method for CWE calculation in five-axis milling based on the distance field and envelope theory is proposed. In the geometry modeling and milling simulation, workpiece surfaces are modeled using sampled distance fields stored in a well-designed octree data structure for efficient memory usage. The inverted trajectory method is used to calculate the tool swept volume, which is subtracted from the in-process workpiece by performing three-stage intersection detection and accelerated Boolean operation. As for the CWE extraction at a specific cutter location, the feasible contact arcs derived from the cutter surfaces based on the envelop theory are used as geometry primitives to intersect the in-process workpiece. A new segment-evaluation algorithm is offered to find the intersection points of each feasible contact arc with the workpiece surfaces. Finally, the CWE diagram is obtained by combining the entry and exit immersion angles of the engagement arcs at each axis height. The feasibility of the proposed method for industrial applications is evidenced by two case studies conducted on a developed virtual machining simulator. The results of the comparison with the B-rep based method indicate that the proposed method is more efficient while providing good accuracy.

The increasing availability of both indoor positioning services and sensors for 3D data capture, such as RGB-D sensors, allows the provision of indoor spatial information services for indoor localization-based applications. To efficiently realize these services, the indoor information and the relationships between indoor spaces are required. The recently released Indoor Geography Markup Language (IndoorGML) attempts to represent and exchange geo-information for modeling topology and semantics of indoor spaces. However, it is still challenging to map indoor space features to the IndoorGML-encoded navigation network model directly from colorized 3D points. Therefore, we propose a semantics-guided method for indoor navigation element reconstruction from RGB-D sensor data. First, a hierarchical indoor scene interpretation framework is used for robustly recognizing the architecture structures and doors, respectively. In the developed hierarchical structure, a graph convolutional network-based architectural structure recognition method is adopted to deduce the long-range interactions among primitives for describing the rich physical relationships in the real world. Its output is the produced initial annotated results, from which doors as the common openings are further detected using a U-Net-based door recognition method. This enables to effectively provide the semantic guidance for the cellular representation of the indoor space and its topological reconstruction. Second, an adaptive architectural structure-guided room segmentation method is developed by combining distance transform and watershed segmentation to determine cellular spaces according to the definition in IndoorGML. Third, taking the different states of doors into consideration, a door-guided topological relationship reconstruction method is proposed to achieve the network graph representation of indoor environments. In this context, a simulated door model is designed to correct and update the true position of a door leaf, and a virtual door is defined to optimize the topological analysis. As a consequence, an IndoorGML-encoded navigation network model is generated, which can be used as the base for indoor navigation applications independent of the platform. Experiments are performed on the public Stanford large-scale 3D Indoor Spaces Dataset to verify the robustness and effectiveness of the proposed method both qualitatively and quantitatively. Results indicate the capability of the proposed method in automatically reconstructing indoor navigation elements of Manhattan-world indoor environments from RGB-D sensor data.

We prove that the 2n-neighbourhood in an n-dimensional digital space is decomposed into the 2 ( n − 1 ) -neighbourhoods in the mutually orthogonal ( n − 1 ) -dimensional digital spaces. This decomposition and construction relation of the neighbourhoods and objects implies that morphological operations in an n-dimensional digital space can be computed as the union of one- and two-dimensional morphological operations on isothetic digital lines and planes intersecting with the digital object in the digital space.

Scene understanding of high resolution aerial images is of great importance for the task of automated monitoring in various remote sensing applications. Due to the large within-class and small between-class variance in pixel values of objects of interest, this remains a challenging task. In recent years, deep convolutional neural networks have started being used in remote sensing applications and demonstrate state of the art performance for pixel level classification of objects. \textcolor{black}{Here we propose a reliable framework for performant results for the task of semantic segmentation of monotemporal very high resolution aerial images. Our framework consists of a novel deep learning architecture, ResUNet-a, and a novel loss function based on the Dice loss. ResUNet-a uses a UNet encoder/decoder backbone, in combination with residual connections, atrous convolutions, pyramid scene parsing pooling and multi-tasking inference. ResUNet-a infers sequentially the boundary of the objects, the distance transform of the segmentation mask, the segmentation mask and a colored reconstruction of the input. Each of the tasks is conditioned on the inference of the previous ones, thus establishing a conditioned relationship between the various tasks, as this is described through the architecture's computation graph. We analyse the performance of several flavours of the Generalized Dice loss for semantic segmentation, and we introduce a novel variant loss function for semantic segmentation of objects that has excellent convergence properties and behaves well even under the presence of highly imbalanced classes.} The performance of our modeling framework is evaluated on the ISPRS 2D Potsdam dataset. Results show state-of-the-art performance with an average F1 score of 92.9\% over all classes for our best model., Accepted for publication to the ISPRS Journal of Photogrammetry and Remote Sensing

This paper addresses the challenge of learning spatial context for the semantic segmentation of high-resolution aerial images using Deep Convolutional Neural Networks (DCNNs). The proposed solution involves deriving a signed distance map for each semantic class from a ground truth label map and training a DCNN to predict this distance map instead of a score map for each class. Since the distance between a target pixel and its nearest object boundary measures how far the pixel penetrates an object, the distance maps encode spatial context, particularly spatial smoothness. Positive pixel values in the distance maps correspond to the correct class and negative values correspond to the incorrect class. A final label map is derived from the predicted distance maps by selecting the class with the maximum distance. Since neighboring pixels in the distance maps have similar values, the segmentation results are smoother than current approaches. The results are shown to be even better than performing post-processing using fully connected Conditional Random Fields (CRFs), a common approach to smoothing the segmentations produced DCNNs. Experimental results on the semantic labeling challenge dataset show the proposed approach outperforms most state-of-the-art methods. Our main contribution, though, is the novel idea of replacing the pixel-wise class score maps of DCNNs with distance maps. This is therefore orthogonal and complementary to other techniques employed by the state-of-the-art methods and could therefore be used to improve upon them.

The feasibility of processes is a well-used notion with several definitions in the literature according to each context. This is understood as the region of operative variables where phenomena of processes occur. In this work, we propose a definition for the feasibility set and explain an algorithm to characterize efficiently its shape and size. Additionally, we define a feasibility index to quantify the belonging grade of a point inside the feasible set, instead of the yes/no usual belonging function. Finally, this paper shows the use of previous concepts for control proposes. In an example, we found the set-point for a process through an optimization problem, guaranteeing the feasibility in the presence of disturbances and improving its productivity.

Handwriting style of an individual will be usually varying from other individuals. The degree of complexity involved in recognition of a handwritten character of south Indian languages is high due to the presence of compound characters. Furthermore the complexity of interpreting handwritten text aggravates due to irregular handwriting styles. Building of datasets for training the database in such environments is tremendous and requires a lot of manual data processing and other preliminary tasks. The major contribution focuses on creation of morphable feature space for addressing handwritten recognition problem. In this paper, techniques useful for simplifying dataset preparation procedures along with a hybrid recognition approach for improvising recognition accuracies of Telugu handwritten characters are proposed. The techniques include text document segmentation, automatic cropping and pincushion and distance transformation based recognition approach. A feature vector is generated from the normalized Gabor features are extracted from pincushion and distance transform models of a character image and classified using Ada boost classifier with a recognition accuracy of 89%.

The watershed analysis has been widely used to segment contacting particles in volumetric images obtained from X-ray Computed Tomography (X-ray CT). However, the watershed analysis cannot discriminate between contacts of two particles and “necks” of peanut-shaped particles. Then, peanut-shaped particles are mistakenly oversegmented as two particles. To addresses this issue, this study developed an improved watershed analysis, which defines a dimensionless parameter α to discriminate contacts and necks. An image morphological reconstruction technique was developed to modify the distance map based on the parameter α. The watershed transform was performed on a modified distance map to overcome oversegmentation. The accuracy and effectiveness of the proposed technique were validated by six sand specimens. The influence of oversegmentation on particle size and shape characterizations were also demonstrated. The results showed that the improved 3D watershed analysis can effectively segment 3D particle contacts while preserving the continuity of necks for different granular soils.

The objective of this study was to determine the effects of flow rates and layer thicknesses for the aggregates on the estimation of the aggregate gradation of an asphalt mixture based on machine vision. The watershed algorithm based on distance transform and concave point detection algorithm were synthetically used to split the touching particles. Increasing the flow rate overall decreased the prediction accuracy of aggregate gradation by image segmentation; the prediction accuracy decreased with the increase of the layer thickness. The prediction accuracy of the segmentation was better than that of the online detection of the asphalt mixture plant.

We develop a fully parallel numerical method which quickly performs 2D and 3D segmentation on GPU to extract anatomical structures from medical images. The algorithm solves the level set equations completely within a Lattice Boltzmann model (LBM). Compared with existing LBM-based segmentation approaches, a parallel distance field regularization is added to the LBM computing scheme to keep computation stable with large time step iteration. This approach also avoids external regularization which has been a major impediment to direct parallelization of level set evolution with LBM. It allows the whole computing process to be efficiently executed on GPU. Moreover, the method can be incorporated with different image features to adopt in various image segmentation tasks. Therefore, our method enables fully GPU accelerated geometric extraction from medical images, leading to high computing performance which is demanded in many practical applications. This method is used to exactly accurate 2D and 3D anatomical structures from many real world CT and MRI images. The achieved results can also directly feed required boundary information to LBM-based hemodynamics simulation.

Railway location design is a complex and time-consuming task in which the intricate interactions among railway alignment and station locations must be considered. However, most optimization methods emphasize either alignment optimization or station locations optimization while ignoring the coupling constraints for railway alignment and station locations. In addition, these methods are mainly applied to plain areas with relatively simple topographies and often fail to find feasible alternatives in complex mountainous areas. This paper proposes a concurrent optimization method for railway alignment and station locations. Coupling constraints for railway alignment and station locations are formulated and addressed, and station locations are generated while searching the railway alignment. The method can be applied for more general terrains, including complex mountainous areas. The effectiveness of the method is verified through a real-world case study in a complex mountainous area. The results show that the proposed method can concurrently find the optimal railway alignment and station locations for specific objectives and multiple constraints and provide various promising alternatives.

In low permeability reservoirs, such as shale oil and tight oil, the natural fractures are critical and primary conduit for the flow of oil and gas. The fluid flow is primarily in the fractures and the matrix usually serves as storage. To exploit these unconventional reservoirs efficiently, an optimized well system needs to be built to maximize the profits. Multilateral well is a kind of well with several laterals from one mainbore, which can potentially optimize the production. In this study, we develop a novel multilateral well optimization method for determining the drilling trajectories and configuration in complex fractured reservoirs. To penetrate more fractures for the production improvement, the objective function is to maximize the ratio between the total length of effectively connected fractures to the well and the optimized well length. A connectivity map is constructed based on the topological relationship among discrete fractures such that the region near a large interconnected cluster is given a high value of importance. Then, the fast marching method is employed to generate a distance map based on the connectivity field. The connectivity map will be altered by shading the cluster that has been connected to the well, and the distance map will also be updated so that the next zone of importance can be recognized. Different optimized lateral trajectories and complete configuration are obtained through iterations by updating the connectivity map, while considering lateral interferences. Specific procedures are further demonstrated through an optimization example. Different multilateral well configurations are optimized and compared. Finally, an optimized well configuration is obtained for the specific developed reservoir. The proposed method is verified through a series of benchmark tests of simple geometries and comparison with conventional straight wells. Results show that a quadlateral well can be the most approximate configuration for the fracture system studied. The results of this paper can have implications for well drilling in subsurface energy systems.

PURPOSE/OBJECTIVE(S) During prostate high-dose-rate (HDR) brachytherapy, physicians select needle positions in a peripheral loading technique based on experience but without knowledge of the achievable dose distribution. Sub-optimal needle placement may lead to unfavorable dose distributions even after plan optimization. We propose a new deep learning-based method to predict HDR needle position for prostate HDR brachytherapy. MATERIALS/METHODS The proposed framework consists of three major steps: (1) deformable registration via registration network (Reg-Net), (2) multi-atlas ranking and (3) needle regression. To model the global spatial relationship among multiple organs, binary masks of the target and organs at risk are transformed into distance maps which describe the distance of each local voxel to the organ surfaces. Reg-Net is utilized to deformably register the distance maps from multi-atlas set to match a patient's distance map and then bring needle maps from multi-atlas to this patient via spatial transformation. Several criteria are used for multi-atlas ranking including prostate volume similarity, multi-organ semantic image similarity and needle position criteria. Finally, needle regression is used to refine the final needle positions. A retrospective study of consecutively treated patients was used to evaluate the feasibility of the proposed method. We performed a five-fold cross validation to evaluate the proposed method. We generated a new dose plan for each patient based on predicted needle location. Target and organ dose volume histogram (DVH) metrics were used to quantify the difference between the clinical and predicted needle plans. All plans were normalized to prostate V100 of 95%. RESULTS Ninety predicted needle plans were compared to clinical plans. In each case, the needle prediction algorithm completed within 1 minute. See table for comparison of target and organ DVH metrics (mean and standard deviation). Predicted needle plans had slightly greater target dose heterogeneity. The RTOG constraints of bladder V75% < 1 cc, rectum V75% < 1cc, and urethra V125% < 1 cc were met in all predicted plans. CONCLUSION It is feasible to use this novel deep-learning-based method to predict needle locations for HDR prostate brachytherapy a priori. This strategy merits further study to improve utilization and quality of prostate brachytherapy.

We propose an approach for real-time shallow water simulation, building upon the virtual pipes model with multi-layered heightmaps. Our approach introduces the use of extended pipes that are capable of resolving flows through fully flooded passages, which is not possible using current multi-layered techniques. We extend the virtual pipe method with a physically-based viscosity model that is both fast and stable. Our viscosity model is integrated implicitly without the expense of solving a large linear system. Despite the few simplifications necessary to achieve a real-time viscosity model, we show that our new viscosity model produces results that match the behavior of an offline fluid-implicit particle (FLIP) simulation for various viscosity values. The liquid is rendered as a triangular mesh surface built from a heightmap. We propose a novel surface optimization approach that prevents interpenetrations of the liquid surface with the underlying terrain geometry. To improve the realism of small-scale scenarios, we present a meniscus shading approach with a view-dependent adjustment of the liquid surface normals based on a distance field. Our implementation runs in real time on various scenarios of roughly 10 × 10 cm at a resolution of 0.5 mm, with up to five layers.

Counting colonies is usually used in microbiological analysis to assess if samples meet microbiological criteria. Although manual counting remains gold standard, the process is subjective, tedious, and time-consuming. Some developed automatic counting methods could save labors and time, but their results are easily affected by uneven illumination and reflection of visible light. To offer a method which counts colonies automatically and is robust to light, we constructed a convenient and cost-effective system to obtain images of colonies at near-infrared light, and proposed an automatic method to detect and count colonies by processing images. The colonies cultured by using raw cows' milk were used as identification objects. The developed system mainly consisted of a visible/near-infrared camera and a circular near-infrared illuminator. The automatic method proposed to count colonies includes four steps, i.e., eliminating noises outside agar plate , removing plate rim and wall, identifying and separating clustered or overlapped colonies, and counting colonies by using connected region labelling, distance transform, and watershed algorithms, etc. A user-friendly graphic user interface was also developed for the proposed method. The relative error and counting time of the automatic counting method were compared with those of manual counting. The results showed that the relative error of the automatic counting method was −7.4%~ + 8.3%, with average relative error of 0.2%, and the time used for counting colonies on each agar plate was 11–21 s, which was 15–75% of the time used in manual counting, depending on the numbers of colonies on agar plates. The proposed system and automatic counting method demonstrate promising performance in terms of precision, and they are robust and efficient in terms of labor- and time-savings.

With the wide use of sophisticated image editing tools, digital image manipulation becomes very convenient and easy, which makes the detection of image tampering operations significant. Image splicing, which refers to a selected region from an image is cut and pasted onto another image, is a ubiquitous image tampering operation. In this paper, based on the finding that the textures and edges can affect the local estimation of noise variance, we propose a novel image splicing detection method via noise level function. Specifically, the test image is first segmented into non-overlapping blocks and the noise variance and the sharpness of each block are calculated. Then, the noise level function, which reflects the relationship between the noise variances and the sharpness of blocks is estimated. The goal of this function is to generate a distance map to describe the minimum distances from the blocks to the fitted curve. The blocks which not be constrained by this estimated noise level function will be distinct in the distance map so that they can be regarded as spliced regions. Finally, contextual information is additionally used to refine the detection result. Extensive experiments demonstrate the superiority of our proposed method in both quantitative and qualitative metrics when compared with the state-of-the-art approaches.

For personal digital libraries as well as automatically acquired image collections, traditional text and metadata based approaches for image retrieval are not sufficient. Commonly, these methods lack detailed descriptions that could be used for searching the required image. In digital libraries, content based image retrieval (CBIR) methods are required to support better image search. A highly robust and efficient shape descriptor based CBIR model has been proposed in this work. Canny edge detection algorithm is employed to identify strong key points on the edges. For key point set formation, the generalized distance transform scheme has been used. Combination of shape and key point identification are used to make proposed CBIR system more robust. Extracted features are fed to Support Vector Machine (SVM) classifier. For retrieval we used similarity matching using Euclidean distance metric. The proposed model provides superior performance while comparing with existing retrieval models.

Localization in unknown environments is a fundamental requirement for robots. Egomotion estimation based on visual information is a hot research topic. However, most visual odometry (VO) or visual Simultaneous Localization and Mapping (vSLAM) approaches assume static environments. To achieve robust and precise localization in dynamic environments, we propose a novel VO based on edges and points for RGB-D cameras. In contrast to dense motion segmentation, sparse edge alignment with distance transform (DT) errors is adopted to detect the states of image areas. Features in dynamic areas are ignored in egomotion estimation with reprojection errors. Meanwhile, static weights calculated by DT errors are added to pose estimation. Furthermore, local bundle adjustment is utilized to improve the consistencies of the local map and the camera localization. The proposed approach can be implemented in real time. Experiments are implemented on the challenging sequences of the TUM RGB-D dataset. The results demonstrate that the proposed robust VO achieves more accurate and more stable localization than the state-of-the-art robust VO or SLAM approaches in dynamic environments.

Object skeleton is a useful geometric tool for shape analysis tasks. It encodes the topological structure of the primitive shape and preserves a geometric cue as well. Skeletonization is a seemingly simple but difficult research problem. A desirable skeletonization algorithm has to be topologically complete, insensitive to boundary noise, without any branch pruning and free of user-specified parameters. In this paper, we propose a novel method based on the heat equation to extract skeletons assuming that the input is a binary image. Based on the connection between the skeleton and ridge lines, we use the smooth heat diffusion height surface to approximate the real distance field, and then extract the ridge lines of the surface as the output skeleton. Different from the existing approaches, the proposed method in this paper has the above-mentioned excellent properties and can capture the clean and stable skeleton directly. Extensive experimental results show that the new approach can yield better skeletons than the state-of-the-art.

We propose a novel method for 3D mesh labeling based on a deep learning approach. We train two deep networks to produce initial labels and semantic boundary maps for test meshes. By using dropout technique, discriminative features can be extracted from our deep networks to improve mesh labeling and boundary detection. Given the detected boundary map, a smoother distance field with closed boundary depiction is calculated for succeeding optimization. Then, based on the initial labels, we obtain the final smooth results through a graph-cut optimization guided by the semantic boundary distance field. With the semantic boundary guidance, labeling is improved distinctly, especially, when large mislabeling regions appear or the boundary of initial labels is not reliable. Furthermore, our algorithm is robust to mesh noise, and can handle mixed dataset with meshes from different categories effectively. Experimental results show that our method outperforms the state-of-the-art methods on public benchmarks.

Purpose Automating and standardizing the contouring of clinical target volumes (CTVs) can reduce interphysician variability, which is one of the largest sources of uncertainty in head and neck radiation therapy. In addition to using uniform margin expansions to auto-delineate high-risk CTVs, very little work has been performed to provide patient- and disease-specific high-risk CTVs. The aim of the present study was to develop a deep neural network for the auto-delineation of high-risk CTVs. Methods and Materials Fifty-two oropharyngeal cancer patients were selected for the present study. All patients were treated at The University of Texas MD Anderson Cancer Center from January 2006 to August 2010 and had previously contoured gross tumor volumes and CTVs. We developed a deep learning algorithm using deep auto-encoders to identify physician contouring patterns at our institution. These models use distance map information from surrounding anatomic structures and the gross tumor volume as input parameters and conduct voxel-based classification to identify voxels that are part of the high-risk CTV. In addition, we developed a novel probability threshold selection function, based on the Dice similarity coefficient (DSC), to improve the generalization of the predicted volumes. The DSC-based function is implemented during an inner cross-validation loop, and probability thresholds are selected a priori during model parameter optimization. We performed a volumetric comparison between the predicted and manually contoured volumes to assess our model. Results The predicted volumes had a median DSC value of 0.81 (range 0.62-0.90), median mean surface distance of 2.8 mm (range 1.6-5.5), and median 95th Hausdorff distance of 7.5 mm (range 4.7-17.9) when comparing our predicted high-risk CTVs with the physician manual contours. Conclusions These predicted high-risk CTVs provided close agreement to the ground-truth compared with current interobserver variability. The predicted contours could be implemented clinically, with only minor or no changes.

This study presents a new method to extract meaningful descriptors of gray-scale texture images using Minkowski morphological dilation based on the L p metric. The proposed approach is motivated by the success previously achieved by Bouligand–Minkowski fractal descriptors on texture classification. In essence, such descriptors are directly derived from the morphological dilation of a three-dimensional representation of the gray-level pixels using the classical Euclidean metric. In this way, we generalize the dilation for different values of p in the L p metric (Euclidean is a particular case when p = 2 ) and obtain the descriptors from the cumulated distribution of the distance transform computed over the texture image. The proposed method is compared to other state-of-the-art approaches (such as local binary patterns and textons for example) in the classification of two benchmark data sets (UIUC and Outex). The proposed descriptors outperformed all the other approaches in terms of rate of images correctly classified. The interesting results suggest the potential of these descriptors in this type of task, with a wide range of possible applications to real-world problems.

Furrow irrigation, which is conducted by creating parallel channels along the field length, is a cultivation method widely used for growing row crops such as hot pepper, garlic, soybean and tree crops. These artificially structured parallel channels, commonly referred to as ridge-furrow, can provide guidance to autonomous tractors with its characteristic of undulating surface. This study reports the development of a stereovision-based guidance line detection system applicable to ridge-furrow cropping fields. The algorithm implemented in the detection system consisted of two different phases, i.e., splitting depth images into two parts (ridge and furrow) and extracting a guidance line from the split images. Through the image binarization method based on a distance transform and image segmentation method, the depth image was divided into two regions of ridge and furrow and the boundary points of each region were then detected. The second phase extracted a guidance line from the detected boundary points based on linear regression. The guidance lines detected by the developed algorithm were compared with those manually labelled, and the results were RMSEs of 0.02 m and 0.63 degree in lateral deviation and heading angle, respectively. Further, the stereo camera was installed on a tractor and field tests were proceeded on a straight and regularly spaced ridge and furrow field. As a result, the RMSE of lateral deviation measured by a RTK-GPS was 1.37 cm at 3 km/s.

Text-line extraction (TLE) is the process of segmenting a document page into lines of text for processing by modules such as language and writer identification or Optical Character Recognition (OCR). Designing of an appropriate TLE method is always a challenging research problem especially in the domain of unconstrained handwritten documents. This is because of the vast number of potential interactions between the text lines. For example, these lines are not always straight, lines written close to each other can overlap with ascenders and descenders, and lines can interact with other content on the page. In this paper, we present a novel language-independent text-line extraction method for unconstrained handwritten documents which handles complexities such as touching and multi-skewed text lines, overlapping characters and irregular inter-line spacing. Our method preprocesses the document pages using a distance transform based method and uses a novel path detection algorithm to separate individual text-line. The proposed method has been tested on six standard datasets which are publicly available and the experimental results show that our method achieves a promising accuracy over state-of-the-art TLE methods.

We propose a novel algorithm for segmenting cells of the cornea endothelium layer on confocal microscope images. To get an inter-cellular space with minimum gray-scale value and to enhance cell borders, we apply a difference of Gaussian filter before image binarization by thresholding with the minimum gray-scale value. Removal of segmented noise and artifacts is performed by automatic thresholding (using an image frequency analysis to obtain a global threshold value per image). Final segmentation of cells is achieved by fitting the largest inscribed circles into the centers of cell regions defined by the distance map of the binary images. Parameters of interest such as cell count and density, pleomorphism, polymegathism, and F-measure are computed on a publicly available data-set (Confocal Corneal Endothelial Microscopy Data Set - Rotterdam Ophthalmic Data Repository) and compared against the results of the segmentation methods included with the data set, and the results of state of the art automatic methods. The obtained results achieve higher accuracy compared to the results of the segmentation included with the data set (e.g., -proposed versus dataset in R2 and mean relative error-, cell count: 0.823, − 0.241 versus 0.017, 0.534; cell density: 0.933, − 0.067 versus 0.154, 0.639; cell polymegathism: 0.652, − 0.079 versus 0.075, 0.886; cell pleomorphism: 0.242, − 0.128 versus 0.0352, − 0.222, respectively), and are in good agreement with the results of the state of the art method.

In this paper, we present a novel spatiotemporal salient object detection method to produce high-quality saliency maps. The gradient of optical flow is adopted to coarsely locate the boundaries of salient object and the gray-weighted distance transform is adopted to highlight the whole salient object for a temporal saliency map. Furthermore, a confidence-guided energy function is proposed to adaptively fuse spatial and temporal saliency maps. Based on these efforts, our method can achieve good performance for complex scenes such as cluster backgrounds and non-rigid deformation. Experimental results on two benchmark datasets demonstrate the efficiency of the proposed saliency method.

Spatially explicit information on urban tree species distribution is crucial for green infrastructure management in cities. This information is usually acquired with ground-based surveys, which are time-consuming and usually cover limited spatial extents. The combination of machine learning algorithms and remote sensing images has been hailed as a promising way to map tree species over broad areas. Recently, convolutional neural networks (CNNs), a type of deep learning method, have achieved outstanding results for tree species discrimination in various remote sensing data types. However, there is a lack of studies using CNN-based methods to produce tree species composition maps, particularly for tropical urban settings. Here, we propose a multi-task CNN to map tree species in a highly diverse neighborhood in Rio de Janeiro, Brazil. Our network architecture takes an aerial photograph (RGB bands and pixel size = 0.15 m) and delivers two outputs: a semantically segmented image and a distance map transform. In the former, all pixel positions are labeled, while in the latter, each pixel position contains the Euclidean distance to the crown boundary. We developed a post-processing approach that combines the two outputs, and we classified nine and five tree species with an average F1-score of 79.3 ± 8.6% and 87.6 ± 4.4%, respectively. Moreover, our post-processing approach produced a realistic tree species composition map by labeling only pixels of the target species with high class membership probabilities. Our results show the potential of CNNs and aerial photographs to map tree species in highly diverse tropical urban settings, providing valuable insights for urban forest management and green spaces planning.

Railway design is complex and closely linked to environmental concerns. To solve this problem, a two-stage method considering three categories of environmental factors (topography, ecology and geology) is proposed and demonstrated by being applied to a real-world case in China. The first stage focuses on environmental impact assessment. An elevation accessibility map is generated by determining railway spatially-reachable ranges. Then, the three categories of environmental factors are divided into 12 sub-factors and their spatial relations with railways are analyzed using a GIS. After that, an environmental suitability map is produced by combining the influences of these sub-factors with a multi-criteria analytical hierarchy process. The second stage focuses on automated railway design. The study area is first narrowed based on the two maps to determine feasible search spaces. Then, a distance transform algorithm is customized to search for railway alignments. During the search, a multi-criteria tournament decision method is integrated to optimize alignment solutions. Lastly, the application results of our two-stage method are analyzed. The outcomes reveal that the two environment-related maps provide effective descriptions of the study area. Through comparisons between the computer-generated railway and the best alternative produced by experienced designers, improvements of our method are also discussed.

Monte Carlo localization (MCL) may fail to localize an arbitrarily moved mobile robot under extreme disturbances. Inspired by the strategy of finding a missing person (SFMP), this paper proposes an efficient re-localization solution to achieve enhanced recovery speed and success rate. With optimized distribution and number of random particle generation, the proposed SFMP-based re-localization ensures the existence of particles in where the robot appears again, which improves the robustness of MCL. First of all, a pivotal search space selection is designed to find where the robot probably appears. Then, a novel moving distance map is constructed to denote the displacement from the kidnapping point to others, thus narrowing the search space according to the possible robot moving distance. Besides, a time-varying long-short term strategy is proposed to adjust the proportion of random particles, and adaptively regulate the particle number. The effectiveness is verified by real scene experiments.

The overall goal of this study is to develop an effective, simple, aptly computer vision algorithm to detect and count citrus on the tree using image processing techniques, to estimate the yield, and to compare the yield estimation results obtained through several methods. This new citrus recognition and counting algorithm was utilized the color features (or schemes) to present an estimate of the citrus yield, and the corresponding models are developed to provide an early estimation of the citrus yield. Citrus images were taken from Jeju, South Korea during daylight and the citrus recognition and counting algorithm were tested on 84 images which were collected from 21 trees. The citrus counting algorithm consisted of the following steps: convert RGB image to HSV, thresholding, orange color detection, noise removal, watershed segmentation, and counting. Distance transform and marker-controlled watershed algorithms were evaluated for automated watershed segmentation in citrus fruits to obtain good result. A correlation coefficient R 2 of 0.93 was obtained between the citrus counting algorithm and counting performed through human observation. The proposed algorithm showed great potential for early prediction of the yield of single citrus trees and the possibility of its uses for further fruit crops.

A novel image sparse representation method, named NAMlet transform, is proposed by fully considering the structure of the nature images.The NAMlet transform is based on the asymmetric homogeneous blocks, which could preserve the detail information of the images.The NAMlet transform can remove the restrictions of the size of the images. Image sparse representation methods have been widely applied in many image processing fields, such as computer vision, image de-noising, super resolution, and visual tracking. An efficient sparse representation method can improve the accuracy. However, few of the traditional representation methods consider from the point of the anti-packing problem. Thus, these methods are not only restricted by the size of the image, but also lose a great amount of detail information by using a symmetric blocking method. In this paper, we have proposed an image sparse representation method, called NAMlet Transform. The NAMlets are haar-type wavelets, which are based on the non-symmetric homogeneous blocks obtained by the non-symmetry and anti-packing model. In homogeneous blocks, all the pixels are in the same bit-plane. The NAMlet transform can reduce the lost detail information and remove the restrictions of image size. The experiment results show the strong superiority of the NAMlet transform for image representation in comparison with some state-of-the-art image sparse representation methods.

The measurement of spacing via the linear intercept method is a stereology technique for quantifying microstructures. Spacing measurements have traditionally been acquired using manual or semi-automatic methods. However, in recent work, the stereology idea of spacing was shown to be closely related to the computer vision idea of distance. If the distance transform can be defined as providing the minimum distance required at a given location to reach the nearest edge, a spacing transform would be defined as providing the distance required at a given location to reach the desired number of nearest consecutive edges along a linear path. The resultant transformed image provides local spacing data which should be the same as those measured by an expert stereologist. This spacing transform addresses the problem of measuring spacing in an interpretable and easily validated fashion. In this paper, spacing transform is defined, applied to real world images, and validated against traditional stereology methods.

Multiple dilation rapidly deforms object structure using mathematical morphology.Preserving object structure is of paramount importance in pattern recognition.A new geometric-based mechanism for binary image dilation is proposed.Our method exploits Delaunay triangulation; a versatile geometric structure.Our method shows high performance when applied to handwritten digit classification. Mathematical morphology has been of a great significance to several scientific fields. Dilation, as one of the fundamental operations, has been very much reliant on the common methods based on the set theory and on using specific shaped structuring elements to morph binary blobs. We hypothesised that by performing morphological dilation while exploiting geometry relationship between dot patterns, one can gain some advantages. The Delaunay triangulation was our choice to examine the feasibility of such hypothesis due to its favourable geometric properties. We compared our proposed algorithm to existing methods and it becomes apparent that Delaunay based dilation has the potential to emerge as a powerful tool in preserving objects structure and elucidating the influence of noise. Additionally, defining a structuring element is no longer needed in the proposed method and the dilation is adaptive to the topology of the dot patterns. We assessed the property of object structure preservation by using common measurement metrics. We also demonstrated such property through handwritten digit classification using HOG descriptors extracted from dilated images of different approaches and trained using Support Vector Machines. The confusion matrix shows that our algorithm has the best accuracy estimate in 80% of the cases. In both experiments, our approach shows a consistent improved performance over other methods which advocates for the suitability of the proposed method. Display Omitted

To solve the problem of the discontinuity of focus region in fused image based on traditional multi-scale analysis and reduce the complexity of fusion method, an energy-efficient multi-focus image fusion algorithm based on multi-scale neighbor distance analysis and morphology is proposed. First, relative to traditional multi-scale analysis, multi-scale neighbor distance analysis can also effectively extract the details of images. The lowpass subband coefficient and highpass subband coefficient are produced based on it, and, then, all of coefficients are divided into blocks with the same size. Second, a coefficient in the highpass subband is seriously related to corresponding one in the lowpass subband. Based on this, block is compared with pair-based scheme in transform domain by using some new fusion rules. As a result, the focused region of source images are determined, and the initial map is acquired. The mathematical morphology is used for post-processing. Finally, the fused image is obtained with the guidance of the decision map. The experimental results demonstrate that the proposed method is effective and can provide better performance in both fusing multi-focus image and the computational complexity than some state-of-art multi-scale analysis-based methods, such as the nonsubsampled contourlet transform (NSCT), contourlet transform, wavelet transform and lifting stationary wavelet transform (LSWT).

Shape classification is an intriguing and challenging problem that lies at the crossroads of computer vision, geometry processing and machine learning. In this paper, we introduce a graph-theoretic approach for 3D shape classification using graph regularized sparse coding in conjunction with the biharmonic distance map. Our unified framework exploits both sparsity and dependence among the features of shape descriptors in a bid to design robust shape signatures that are effective in discriminating between shapes from different classes. In an effort to coherently capture the similarity between feature descriptors, we use multiclass support vector machines for 3D shape classification on mid-level features that are learned via graph regularized sparse coding. Our experiments on two standard 3D shape benchmarks show that the proposed framework not only outperforms the state-of-the-art methods in classification accuracy, but also provides attractive scalability in terms of computational efficiency.

The pixel based cost computation using the distance transform is proposed.The distance transform gives specific values to the pixel in the textureless region.The stereo matching based on the distance transform outperforms in the result image comparing with the conventional method.The disparity error detection and correction methods are also proposed as a post-processing step to enhance the result image. With the great success in three-dimensional (3D) movies, a lot of 3D content have been generated. Depth information is one of the important elements in 3D content generation. Stereo matching methods obtain depth information using the characteristic of binocular disparity. These methods find corresponding points between two images which have different viewpoints to calculate the disparity value. However, these methods have difficulties computing accurate disparity values in the textureless region. Smeared pixels near the edge region also make difficult for the stereo matching. In this paper, we propose a pixel based cost computation for the cross-scale stereo matching using the distance transform to improve these problems. In addition, the disparity error detection and correction methods are also proposed as a post-processing step. As a result, we obtain the enhanced disparity map which is robust to the textureless region and the edge region.

Gross tumor volume (GTV) and clinical target volume (CTV) delineation are two critical steps in the cancer radiotherapy planning. GTV defines the primary treatment area of the gross tumor, while CTV outlines the sub-clinical malignant disease. Automatic GTV and CTV segmentation are both challenging for distinct reasons: GTV segmentation relies on the radiotherapy computed tomography (RTCT) image appearance, which suffers from poor contrast with the surrounding tissues, while CTV delineation relies on a mixture of predefined and judgement-based margins. High intra- and inter-user variability makes this a particularly difficult task. We develop tailored methods solving each task in the esophageal cancer radiotherapy, together leading to a comprehensive solution for the target contouring task. Specifically, we integrate the RTCT and positron emission tomography (PET) modalities together into a two-stream chained deep fusion framework taking advantage of both modalities to facilitate more accurate GTV segmentation. For CTV segmentation, since it is highly context-dependent-it must encompass the GTV and involved lymph nodes while also avoiding excessive exposure to the organs at risk-we formulate it as a deep contextual appearance-based problem using encoded spatial distances of these anatomical structures. This better emulates the margin- and appearance-based CTV delineation performed by oncologists. Adding to our contributions, for the GTV segmentation we propose a simple yet effective progressive semantically-nested network (PSNN) backbone that outperforms more complicated models. Our work is the first to provide a comprehensive solution for the esophageal GTV and CTV segmentation in radiotherapy planning. Extensive 4-fold cross-validation on 148 esophageal cancer patients, the largest analysis to date, was carried out for both tasks. The results demonstrate that our GTV and CTV segmentation approaches significantly improve the performance over previous state-of-the-art works, e.g., by 8.7% increases in Dice score (DSC) and 32.9mm reduction in Hausdorff distance (HD) for GTV segmentation, and by 3.4% increases in DSC and 29.4mm reduction in HD for CTV segmentation.

We propose a method that use a convolutional neural network (CNN) to estimate human pose by analyzing the projection of the depth and ridge data, which represent local maxima in a distance transform map. To fully utilize the 3D information of depth points, we propose a method to project the depth and ridge data on various directions. The proposed projection method can reduce the 3D information loss, the ridge data can avoid joint drift, and the CNN increases localization accuracy. The proposed method proceeds as follows. (1) We use depth data to segment the human from the background and extract ridge data from human silhouettes. (2) We project the depth and ridge data onto XY, XZ, and ZY planes. (3) ResNet-101 accepts six projected images and use 1 × 1 convolution layers to generate 2D heatmaps and offsets. (4) We generate 2D keypoints per plane by using the soft-argmax operation. (5) We obtain 3D joint positions by using the fully-connected layers. In experiments on the SMMC-10, EVAL, and ITOP datasets, the proposed method achieved the state-of-the-art pose estimation accuracies. The proposed method can eliminate the 3D information loss and drift of joint positions that can occur during estimation of human pose.

The micropore and grain thicknesses of calcium phosphate (CaP) bone substitutes are believed to have strong influence on in vivo biological responses. The thickness measurement is challenging due to complex morphologies of the elongated CaP micropores and grains. This study aimed to develop and verify a novel linear intercept (NLI) algorithm based on SEM images to calculate thicknesses accurately for elongated geometrical features. The standard linear intercept (SLI) algorithm overestimates the thickness of micropores and grains wherever the defined lines are not perpendicular to such geometrical features. The NLI was developed by integrating the standard algorithm with a distance transform map to exclude the overestimation errors. Besides the accurate thickness calculation, the NLI measures the orientation angle of architectural features as an indication for isotropy level. The NLI-based thicknesses of five groups of β-TCP scaffolds were compared and verified with those of a refined centerline (RC) algorithm. The RC algorithm was accurate yet human assisted and very time intensive. Compared with RC algorithm, the NLI-based results were 2 ± 13 and 4 ± 9% (Mean ± SD) lower for average micropore and grain thicknesses, respectively. The NLI results were also compared with two standard and commonly used algorithms. The SLI and maximal-fitted-circle (MFC) algorithms resulted in 72 ± 25 and 91 ± 47% overestimation errors, respectively.

Railway alignment design is complex and time-consuming, especially for mountainous areas where the natural terrain gradient between the start and end points greatly exceeds the maximum allowed design gradient. Existing methodologies can optimize routes in areas with relatively simple topography, but often fail in finding the feasible alternatives in complex mountainous terrain. Thus, a two-phase methodology is proposed for optimizing multi-constrained 3-dimensional railway alignments. We generate various promising paths in the first phase and refine them into final alignments by fitting the required curved sections in the next phase. Firstly, the study area is represented using a 3-dimensional rectangular lattice and a comprehensive geographic information model is specified to store and manage the geographic information in this lattice. Secondly, an objective function is developed for estimating the railway alignment’s comprehensive cost. Thirdly, a multi-constrained distance transform is employed as a new approach for generating optimizing paths through various cells in the lattice. Multiple constraints on geometry, structures and locations are handled in this approach. To avoid possible failures in finding paths in the complex mountain regions due to multiple constraints, an adaptive neighboring mask and a bidirectional scanning strategy are proposed for generating various promising 3-dimensional paths. In the alignment fitting process we form the initial alignment by recursively inserting points of intersection and then optimize the final alignment using the mesh adaptive direct search algorithm. The effectiveness of the approach is verified through a real-world case study in a mountainous area where the natural terrain gradient is nearly triple the maximum allowed design gradient. The results show that this methodology can automatically find various promising alternatives, while satisfying the complex constraints.

A comprehensive 3-D curve skeletonization algorithm using minimum cost pathA non-parametric local significance factor for fuzzy centers of maximal ballsA path cost function ensuring skeletal branches along object centerlinesThe new method outperforms existing ones with respect to accuracy and noisy branchComputation complexity reduced from the number of terminal branches to tree-depth Conventional curve skeletonization algorithms using the principle of Blum's transform, often, produce unwanted spurious branches due to boundary irregularities, digital effects, and other artifacts. This paper presents a new robust and efficient curve skeletonization algorithm for three-dimensional (3-D) elongated fuzzy objects using a minimum cost path approach, which avoids spurious branches without requiring post-pruning. Starting from a root voxel, the method iteratively expands the skeleton by adding new branches in each iteration that connects the farthest quench voxel to the current skeleton using a minimum cost path. The path-cost function is formulated using a novel measure of local significance factor defined by the fuzzy distance transform field, which forces the path to stick to the centerline of an object. The algorithm terminates when dilated skeletal branches fill the entire object volume or the current farthest quench voxel fails to generate a meaningful skeletal branch. Accuracy of the algorithm has been evaluated using computer-generated phantoms with known skeletons. Performance of the method in terms of false and missing skeletal branches, as defined by human experts, has been examined using in vivo CT imaging of human intrathoracic airways. Results from both experiments have established the superiority of the new method as compared to the existing methods in terms of accuracy as well as robustness in detecting true and false skeletal branches. The new algorithm makes a significant reduction in computation complexity by enabling detection of multiple new skeletal branches in one iteration. Specifically, this algorithm reduces the number of iterations from the number of terminal tree branches to the worst case performance of tree depth. In fact, experimental results suggest that, on an average, the order of computation complexity is reduced to the logarithm of the number of terminal branches of a tree-like object.

Display Omitted We introduce an automatic 3D shape morphing method without the need of manually placing anchor correspondence points. Given a source and a target shape, we extract their skeletons and automatically estimate the meaningful anchor points based on their skeleton node correspondences. Based on the anchors, dense correspondences between the interior of source and target shape can be established using earth movers distance (EMD) optimization. Skeleton node correspondence, estimated with a voting-based method, leads to part correspondence which can be used to confine the dense correspondence within matched part pairs. This produces smooth and plausible morphing sequence based on distance field interpolation (DFI). We demonstrate the effectiveness of our algorithm over shapes with large geometric variation and structural difference.

Evaluation of image segmentation algorithms is a crucial task in the image processing field. Generally, traditional objective evaluation measures, such as ME and JS, always give the same treatment to the object pixels and the background pixels in images, which is not reasonable in practical applications. To overcome this problem, a new objective evaluation metric based on the weighted-ROC graph is proposed in this paper. Considering that pixels in different positions may gain different importance, each pixel is given a weight based on its spatial information. The ROC (receiver operating characteristic) graph with weighting strategy is constructed to evaluate the performance of segmentation algorithms quantitatively. The proposed metric focuses on the segmented objects, which is similar to human visual system. Meanwhile, it reserves the robustness of ROC against the region imbalance. The experimental results on various images show that the proposed metric gives more reasonable evaluation results than other metrics. The importance of each pixel is taken into account in the evaluating process.Weighted strategy is applied to the ROC graph.The problem of distorted evaluation on images with region imbalance is eliminated.The assessment results are more in line with the subjective evaluation results.The metric holds for both illumination images and non-uniform illumination images.

Feature descriptors have become an increasingly important tool in shape analysis. Features can be extracted and subsequently used to design robust signatures for shape retrieval, correspondence, classification and clustering. In this paper, we present a graph-theoretic framework for 3D shape clustering using the biharmonic distance map and graph regularized sparse coding. While this work focuses primarily on clustering, our approach is fairly general and can be used to tackle other 3D shape analysis problems. In order to seamlessly capture the similarity between feature descriptors, we perform shape clustering on mid-level features that are generated via graph regularized sparse coding. Extensive experiments are carried out on three standard 3D shape benchmarks to demonstrate the much better performance of the proposed clustering approach in comparison with recent state-of-the-art methods.

A skeleton-based fiber tracing algorithm is described and applied on a specific fibrous material, porous metal fiber sintered sheet (PMFSS), featuring high porosity and curved fibers. The skeleton segments are firstly categorized according to the connectivity of the skeleton paths. Spurious segments like fiber bonds are detected making extensive use of the distance transform (DT) values. Single fibers are then traced and reconstructed by consecutively choosing the connecting skeleton segment pairs that show the most similar orientations and radius. Moreover, to reduce the misconnection due to the tracing orders, a multilevel tracing strategy is proposed. The fibrous network is finally reconstructed by dilating single fibers according to the DT values. Based on the traced single fibers, various morphology information regarding fiber length, radius, orientation, and tortuosity are quantitatively analyzed and compared with our previous results (Wang et al., 2013). Moreover, the number of bonds per fibers are firstly accessed. The methodology described in this paper can be expanded to other fibrous materials with adapted parameters. Keywords: Fiber tracing, Skeleton, Morphology analysis

Hausdorff distance measures the distance between two sets in a metric space. The conventional Hausdorff distance is calculated by using only individual point and each point is equally weighted. The gradient orientation of each point is ignored, which limits the performance of Hausdorff distance in the image registration. Moreover, different points are of different importance and thus should be assigned different weights. This paper proposes a method to register visible and infrared images with modified Hausdorff distance measure, which uses both the position and the gradient orientation of each point. Each point is differently weighted by corner response value of each point. The experimental results demonstrate a better performance of the proposed method for registration of multi-sensor images in comparison with existing methods, which are based on conventional Hausdorff distance by the root of the mean square error (RMSE).

This paper proposed a novel algorithm to extract the skeleton for the objects on three dimensional images with or without noise.Neutrosophic cost function is proposed based on neutrosophic set.Neutrosophic cost function is employed to define the cost between each point on skeleton. A skeleton provides a synthetic and thin representation of three dimensional objects, and is useful for shape description and recognition. In this paper, a novel 3D skeleton algorithm is proposed based on neutrosophic cost function. Firstly, the distance transform is used to a 3D volume, and the distance matrix is obtained for each voxel in the volume. The ridge points are identified based on their distance transform values and are used as the candidates for the skeleton. Then, a novel cost function, namely neutrosophic cost function (NCF) is proposed based on neutrosophic set, and is utilized to define the cost between each ridge points. Finally, a shortest path finding algorithm is used to identify the optimum path in the 3D volume with least cost, in which the costs of paths are calculated using the new defined NCF. The optimum path is treated as the skeleton of the 3D volume. A variety of experiments have been conducted on different 3D volume. The experimental results demonstrate the better performance of the proposed method. It can identify the skeleton for different volumes with high accuracy. In addition, the proposed method is robust to the noise on the volume. This advantage will lead it to wide application in the skeleton detection applications in the real world.

We propose a method for computing Euclidean distance transform (EDT) in 3D images.The method utilizes voxel coverage information to increase precision of EDT.The method can be used with any vector propagation based EDT in 3D.Synthetic tests confirm significant improvement in achieved precision.Both the related binary and the existing coverage based methods are outperformed. Distance transforms (DTs) are, usually, defined on a binary image as a mapping from each background element to the distance between its centre and the centre of the closest object element. However, due to discretization effects, such DTs have limited precision, including reduced rotational and translational invariance. We show in this paper that a significant improvement in performance of Euclidean DTs can be achieved if voxel coverage values are utilized and the position of an object boundary is estimated with sub-voxel precision. We propose two algorithms of linear time complexity for estimating Euclidean DT with sub-voxel precision. The evaluation confirms that both algorithms provide 4-14 times increased accuracy compared to what is achievable from a binary object representation.

In Resin Infusion (RI) processes, the flow front shape progression is mainly conditioned by the initial arrangement of the injection and vent gate line locations and the permeability of the preform. The main goal of this research is to develop fast (not necessarily physically-based) tools at the pre-design stage that could help designers with a suitable arrangement of injection nozzles and vents. This pre-design should then be validated by full-physics simulation or lab test, but could be considered as a suitable starting point in the designing process. RI simulators could eventually be equipped with this kind of pre-design tools as a means to provide very fast (at the cost of a somewhat reduced accuracy) designs. In the approach here presented the pre-design tools are based entirely on geometrical assumptions. Under these hypotheses, and assuming that the vents will be placed on the boundary of the piece, the distance field from this boundary will provide useful information on the optimal position of injection nozzles. In this work, inspired by the concept of medial axis, we propose a numerical technique that computes numerically approximate distance fields by invoking computational geometry concepts that can be used for the estimation of the gate arrangement in infusion processes. Detailed descriptions of the developed algorithm, together with first proofs of its performance are given.