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In remote-sensing image processing tasks, images with higher resolution always result in better performance on downstream tasks, such as scene classification and object segmentation. However, objects in remote-sensing images often have low resolution and complex textures due to the imaging environment. Therefore, effectively reconstructing high-resolution remote-sensing images remains challenging. To address this concern, we investigate embedding context information and object priors from remote-sensing images into current deep learning super-resolution models. Hence, this paper proposes a novel remote-sensing image super-resolution method called Context-Guided Constrained Network (CGC-Net). In CGC-Net, we first design a simple but effective method to generate inverse distance maps from the remote-sensing image segmentation maps as prior information. Combined with prior information, we propose a Global Context-Constrained Layer (GCCL) to extract high-quality features with global context constraints. Furthermore, we introduce a Guided Local Feature Enhancement Block (GLFE) to enhance the local texture context via a learnable guided filter. Additionally, we design a High-Frequency Consistency Loss (HFC Loss) to ensure gradient consistency between the reconstructed image (HR) and the original high-quality image (HQ). Unlike existing remote-sensing image super-resolution methods, the proposed CGC-Net achieves superior visual results and reports new state-of-the-art (SOTA) performance on three popular remote-sensing image datasets, demonstrating its effectiveness in remote-sensing image super-resolution (RSI-SR) tasks. [ABSTRACT FROM AUTHOR]

Active contours model (ACM) has been extensively used in computer vision and image processing. In recent studies, convolutional neural networks (CNNs) have been combined with ACM replacing the user in the process of contour evolution and image segmentation to eliminate limitations associated with ACM dependence on energy functional parameters and initialization. However, prior studies did not aim for automatic initialization, which is addressed in this article. In addition to manual initialization, current methods are highly sensitive to the initial location and fail to delineate borders accurately. We propose a fully automatic image segmentation method to address problems of manual initialization, insufficient capture range, and poor convergence to boundaries, in addition to the problem of assignment of energy functional parameters. We train two CNNs, one of which generating ACM weighting parameters and the other generating a ground truth mask to extract distance transform (DT) and an initialization circle. DT is used to form a vector field pointing from each pixel of the image towards the closest ground truth boundary point. Vector magnitudes are equal to the Euclidean distance between each pixel and the closest ground truth boundary point. We evaluate our method on four publicly available datasets, including two building instance segmentation datasets, i.e., Vaihingen and Bing huts, and two mammography image datasets, INBreast and DDSM-BCRP. Our approach achieves state-of-the-art results in mean Intersection over Union (mIoU), Dice similarity coefficient and Boundary F-score (BoundF) with the values of 92.33%, 92.44%, and 86.57% for Vaihingen dataset, and 87.12%, 86.86%, and 66.91% for Bing huts dataset. We obtained the Dice similarity coefficient values of 94.23% and 90.89% for the INBreast and DDSM-BCRP, respectively. [ABSTRACT FROM AUTHOR]

Visual odometry, which aims to estimate relative camera motion between sequential video frames, has been widely used in the fields of augmented reality, virtual reality, and autonomous driving. However, it is still quite challenging for state-of-the-art approaches to handle low-texture scenes. In this paper, we propose a robust and efficient visual odometry algorithm that directly utilizes edge pixels to track camera pose. In contrast to direct methods, we choose reprojection error to construct the optimization energy, which can effectively cope with illumination changes. The distance transform map built upon edge detection for each frame is used to improve tracking efficiency. A novel weighted edge alignment method together with sliding window optimization is proposed to further improve the accuracy. Experiments on public datasets show that the method is comparable to state-of-the-art methods in terms of tracking accuracy, while being faster and more robust. [ABSTRACT FROM AUTHOR]

This paper presents a major reformulation of a widely used solution for computing the exact Euclidean distance transform of n-dimensional discrete binary shapes. Initially proposed by Hirata, the original algorithm is linear in time, separable, and easy to implement. Furthermore, it accounts for the fastest existing solutions, leading to its widespread use in the state of the art, especially in real-time applications. In particular, we focus on the second step of this algorithm, where the lower envelope of a set of parabolas has to be computed. By leveraging the discrete nature of images, we show that some of those parabolas can be merged into line segments. It reduces the computational cost of the algorithm by about 20% in most practical cases, while maintaining its exactness. To evaluate the proposed improvement on different cases, two state-of-the art benchmarks are implemented and discussed. [ABSTRACT FROM AUTHOR]

In remote-sensing image processing tasks, images with higher resolution always result in better performance on downstream tasks, such as scene classification and object segmentation. However, objects in remote-sensing images often have low resolution and complex textures due to the imaging environment. Therefore, effectively reconstructing high-resolution remote-sensing images remains challenging. To address this concern, we investigate embedding context information and object priors from remote-sensing images into current deep learning super-resolution models. Hence, this paper proposes a novel remote-sensing image super-resolution method called Context-Guided Constrained Network (CGC-Net). In CGC-Net, we first design a simple but effective method to generate inverse distance maps from the remote-sensing image segmentation maps as prior information. Combined with prior information, we propose a Global Context-Constrained Layer (GCCL) to extract high-quality features with global context constraints. Furthermore, we introduce a Guided Local Feature Enhancement Block (GLFE) to enhance the local texture context via a learnable guided filter. Additionally, we design a High-Frequency Consistency Loss (HFC Loss) to ensure gradient consistency between the reconstructed image (HR) and the original high-quality image (HQ). Unlike existing remote-sensing image super-resolution methods, the proposed CGC-Net achieves superior visual results and reports new state-of-the-art (SOTA) performance on three popular remote-sensing image datasets, demonstrating its effectiveness in remote-sensing image super-resolution (RSI-SR) tasks.

Geospatial data analysis often requires the computing of a distance transform for a given vector feature. For instance, in wildfire management, it is helpful to find the distance of all points in an area from the wildfire's boundary. Computing a distance transform on traditional Geographic Information Systems (GIS) is usually adopted from image processing methods, albeit prone to distortion resulting from flat maps. Discrete Global Grid Systems (DGGS) are relatively new low-distortion globe-based GIS that discretize the Earth into highly regular cells using multiresolution grids. In this paper, we introduce an efficient distance transform algorithm for DGGS. Our novel algorithm heavily exploits the hierarchy of a DGGS and its mathematical properties and applies to many different DGGSs. We evaluate our method by comparing its speed and distortion with the distance transform methods used in traditional GIS and general 3D meshes. We demonstrate that our method is efficient and has minimal distortion. [ABSTRACT FROM AUTHOR]

The design of railway alignment and station locations involves two intertwined problems, which makes it a complex and time-consuming task. Especially in mountainous regions, the large 3-dimensional (3D) search spaces, complex terrain conditions, coupling constraints and infinite numbers of potential alternatives of this problem pose many challenges. However, most current optimization methods emphasize either alignment optimization or station locations optimization independently. Only a few methods consider coordinated optimization of alignment and stations, but optimize them sequentially. This paper proposes a concurrent optimization method based on a 3-dimensional distance transform algorithm (3D-DT) to solve this problem. It includes the following components: (1) To optimize the location of stations within specified spacing intervals, a novel perceptual search strategy is proposed and incorporated into the basic 3D-DT optimization process. (2) A combined-alignment-station 3D search neighboring mask is developed and employed to search for both the alignment and stations. In order to implement the perceptual process, two additional kinds of 3D reverse perceptual neighboring masks are also developed and employed in the algorithm. (3) Multiple coupling constraints between alignment and stations are also formulated and addressed during the search process. In this study, the effectiveness of the method is verified through a real-world case study in a complex mountainous region. The optimization results show that the proposed method can find high-quality alternatives satisfying multiple coupling constraints.

Diffuse optical tomography (DOT) leverages near-infrared light propagation through tissue to assess its optical properties and identify abnormalities. DOT image reconstruction is an ill-posed problem due to the highly scattered photons in the medium and the smaller number of measurements compared to the number of unknowns. Limited-angle DOT reduces probe complexity at the cost of increased reconstruction complexity. Reconstructions are thus commonly marred by artifacts and, as a result, it is difficult to obtain an accurate reconstruction of target objects, e.g., malignant lesions. Reconstruction does not always ensure good localization of small lesions. Furthermore, conventional optimization-based reconstruction methods are computationally expensive, rendering them too slow for real-time imaging applications. Our goal is to develop a fast and accurate image reconstruction method using deep learning, where multitask learning ensures accurate lesion localization in addition to improved reconstruction. We apply spatial-wise attention and a distance transform based loss function in a novel multitask learning formulation to improve localization and reconstruction compared to single-task optimized methods. Given the scarcity of real-world sensor-image pairs required for training supervised deep learning models, we leverage physics-based simulation to generate synthetic datasets and use a transfer learning module to align the sensor domain distribution between in silico and real-world data, while taking advantage of cross-domain learning. Applying our method, we find that we can reconstruct and localize lesions faithfully while allowing real-time reconstruction. We also demonstrate that the present algorithm can reconstruct multiple cancer lesions. The results demonstrate that multitask learning provides sharper and more accurate reconstruction. [ABSTRACT FROM AUTHOR]

The detection of mathematical expressions is a prerequisite step for the digitisation of scientific documents. Many different multistage approaches have been proposed for the detection of expressions in document images, that is, page segmentation and expression detection. However, the detection accuracy of such methods still needs improvement owing to errors in the page segmentation of complex documents. This paper presents an end‐to‐end framework for mathematical expression detection in scientific document images without requiring optical character recognition (OCR) or document analysis techniques applied in conventional methods. The novelty of this paper is twofold. First, because document images are usually in binary form, the direct use of these images, which lack texture information as input for detection networks, may lead to an incorrect detection. Therefore, we propose the application of a distance transform to obtain a discriminating and meaningful representation of mathematical expressions in document images. Second, the transformed images are fed into the faster region with a convolutional neural network (Faster R‐CNN) optimized to improve the accuracy of the detection. The proposed framework was tested on two benchmark data sets (Marmot and GTDB). Compared with the original Faster R‐CNN, the proposed network improves the accuracies of detection of isolated and inline expressions by 5.09% and 3.40%, respectfully, on the Marmot data set, whereas those on the GTDB data set are improved by 4.04% and 4.55%. A performance comparison with conventional methods shows the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In our country today, the counting of dried coconuts at the production facilities is done manually, takes a lot of time and is not accurate. The goal of this study is to build an automatic, fast and accurate coconut counting system. The study was conducted on the peeled dried coconut fruit with a diameter of 15 cm to 20 cm using image processing technology and open-source computer vision library - OpenCV library. The algorithm includes four main steps. First, determine the object and the background using the Otsu segmentation method. Next, estimate the distance between the background and the object to determine the closest area to the center of the object. Then, find the contour, determine the center and area of the object to reduce the noise. The watershed segmentation algorithm is used to separate overlapping and stacking objects. Finally, count the number of objects contained in the image. In the initial experimental results, the counting system has had an accuracy of over 95% with processing time per image about 75 ms and the counting capacity of the system is over 2000 fruits/hour has confirmed the efficiency of the proposed method.

Hoverflies (Diptera: Syrphidae) provide an excellent opportunity to study the evolution of Batesian mimicry, where defenseless prey avoid predation by evolving to resemble defended "model" species. Although some hoverflies beautifully resemble their hymenopteran models, others seem to be poor mimics or are apparently nonmimetic. The reasons for this variation are still enigmatic despite decades of research. Here, we address this issue by mapping social‐wasp mimicry across the phylogeny of Holarctic hoverflies. Using the "distance transform" technique, we calculate an objective measure of the abdominal pattern similarity between 167 hoverfly species and a widespread putative model, the social wasp, Vespula germanica. We find that good wasp mimicry has evolved several times, and may have also been lost, leading to the presence of nonmimics deep within clades of good mimics. Body size was positively correlated with similarity to the model, supporting previous findings that smaller species are often poorer mimics. Additionally, univoltine species were less accurate wasp mimics than multivoltine and bivoltine species. Hence, variation in the accuracy of Batesian mimics may reflect variation in the opportunity for selection caused by differences in prey value or signal perception (influenced by body size) and phenology or generation time (influenced by voltinism). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

To explore the problem of distance transformations while obstacles existing, this paper presents an obstacle-avoiding Euclidean distance transform method based on cellular automata. This research took the South China Sea and its adjacent sea areas as an example, imported the data of land-sea distribution and target points, took the length of the shortest obstacle-avoiding path from current cell to the target cells as the state of a cellular, designed the state transform rule of each cellular that considering a distance operator, then simulated the propagation of obstacle-avoiding distance, and got the result raster of obstacle-avoiding distance transform. After analyzing the effect and precision of obstacle avoiding, we reached the following conclusions: first, the presented method can visually and dynamically show the process of obstacle-avoiding distance transform, and automatically calculate the shortest distance bypass the land; second, the method has auto-update mechanism and each cellular can rectify distance value according to its neighbor cellular during the simulation process; at last, it provides an approximate solution for exact obstacle-avoiding Euclidean distance transform and the proportional error is less than 1.96%. The proposed method can apply to the fields of shipping routes design, maritime search and rescue, etc.

Recognition of overlapping objects is required in many applications in the field of computer vision. Examples include cell segmentation, bubble detection and bloodstain pattern analysis. This paper presents a method to identify overlapping objects by approximating them with ellipses. The method is intended to be applied to complex-shaped regions which are believed to be composed of one or more overlapping objects. The method has two primary steps. First, a pool of candidate ellipses are generated by applying the Euclidean distance transform on a compressed image and the pool is filtered by an overlaying method. Second, the concave points on the contour of the region of interest are extracted by polygon approximation to divide the contour into segments. Then, the optimal ellipses are selected from among the candidates by choosing a minimal subset that best fits the identified segments. We propose the use of the adjusted Rand index, commonly applied in clustering, to compare the fitting result with ground truth. Through a set of computational and optimization efficiencies, we are able to apply our approach in complex images comprised of a number of overlapped regions. Experimental results on a synthetic data set, two types of cell images and bloodstain patterns show superior accuracy and flexibility of our method in ellipse recognition, relative to other methods. [ABSTRACT FROM AUTHOR]

Strand proposed a distance-based thinning algorithm for computing sur-face skeletons on the body-centered cubic (BCC) grid. In this paper, we present two modified versions of this algorithm that are faster than the original one, and less sensitive to the visiting order of points in the sequential thinning phase. In addition, a novel algorithm capable of producing curve skeletons is also reported. [ABSTRACT FROM AUTHOR]

Human action recognition based on silhouette images has wide applications in computer vision, human computer interaction and intelligent surveillance. It is a challenging task due to the complex actions in nature. In this paper, a human action recognition method is proposed which is based on the distance transform and entropy features of human silhouettes. In the first stage, background subtraction is performed by applying correlation coefficient based frame difference technique to extract silhouette images. In the second stage, distance transform based features and entropy features are extracted from the silhouette images. The distance transform based features and entropy features provide the shape and local variation information. These features are given as input to neural networks to recognize various human actions. The proposed method is tested on three different datasets viz., Weizmann, KTH and UCF50. The proposed method obtains an accuracy of 92.5%, 91.4% and 80% for Weizmann, KTH and UCF50 datasets respectively. The experimental results show that the proposed method for human action recognition is comparable to other state-of-the-art human action recognition methods. [ABSTRACT FROM AUTHOR]

The processing of multispectral images acquired with embedded cameras in unmanned aerial vehicles (drones) has brought new opportunities for precision agriculture. In this study a method for evaluating the number of corn plants (Zea mays L) in a crop area is presented. Plant density is one of the most important yield factors, yet its precise measurement after the emergence of plants is impractical in large and medium-scale production, since significant amount of labor is required. For validation, a dataset of spectral images was gathered from flights over an agricultural area, and digital image processing techniques were applied, taking into account the concept of intelligent processing. Therefore, pattern recognition and models to aid decision-making through machine learning were also used. After image acquisition, the processing of orthomosaics in the spectral channels, i.e., red (R), green (G), and blue (B), was performed, making it possible to register and organize all the images. Likewise, techniques for geometric transformation, brightness, and contrast adjustments were evaluated globally, whereas local adjustments were evaluated based on the use of adaptive equalization techniques, which were explored based in the choice of the HSV color space. For the post-processing step, segmentation based on the best observed color threshold technique, in conjunction with Gaussian filtering and morphological operations, were considered. To enable pattern recognition, techniques that use distance maps were evaluated, considering the use of Euclidean distance. Thus, the locations of canopy patterns in maize plants were studied using a template matching algorithm and Chamfer pattern mask. For feature extraction, chain code and circular pattern map techniques were considered. The analyses made it possible to establish vectors of features based on patterns related to the number of maize plants occurrences. Finally, three calibration steps were considered, one related to the plant height versus the canopy opening radius, other related to the number of maize plants for each position in the crop area versus the radii identified by the developed model, and the third related to the cross-correlation between the plant counting by human vision and the new method. In addition, the classification step was established using a set of classifiers based on support vector machine (SVM). Results have shown an accurate and timely counting methodology for maize plants, which can guide cultivation to ensure high yield. The results showed that as a new method it can effectively count the number of maize plants with an average accuracy rate equal to 88.47%. Besides, both selected SVM classifiers have presented accuracy higher than 84% and precision higher than 83%. Furthermore, the cross-correlation between the plant counting by human vision and the new method has presented a linear correlation coefficient equal to 0.98. Thus, the developed method proved to be adequate for counting the maize plants in the post-emergence stage. • Patch crops are locally equalized by color spaces for uniformity of their intensities. • A color-based segmentation using HSV is used to separate maize plants and soil. • Distance transform is used to locate the central lines of the maize crop. • Template matching with Chamfer mask were used to detect maize plants post-emergence V2. [ABSTRACT FROM AUTHOR]

Abstract Distance transform, a central operation in image and video analysis, involves finding the shortest path between feature and non-feature entries of a binary image. The process may be implemented using chamfer-based sequential algorithms that apply small-neighborhood masks to estimate the Euclidean metric. Success of these algorithms depends on the cost function used to optimize chamfer weights. And, for years, mean absolute error and mean squared error have been used for optimization. However, studies have revealed weaknesses of these cost functions—sensitivity against outliers, lack of symmetry, and biasedness—which limit their application. In this work, we have proposed a robust and a more accurate cost function, symmetric mean absolute percentage error, which attempts to address some weaknesses. The proposed function averages the absolute percentage errors in a set of measurements and offers interesting mathematical properties (smoothness, differentiability, boundedness, and robustness) that allow easy interpretation and analysis of the results. Numerical results show that chamfer masks designed under our optimization criterion generate lower errors. The present work has also proposed an automatic algorithm that converts coefficients of the designed real-valued masks into integers, which are preferable in most practical computing devices. Lastly, we have modified the chamfer algorithm to improve its speed and then embedded the proposed weights into the algorithm to compute distance maps of real images. Results show that the proposed algorithm is faster and uses fewer number of operations compared with those consumed by the classical chamfer algorithm. Our results may be useful in robotics to address the matching problem.

Geospatial data analysis often requires the computing of a distance transform for a given vector feature. For instance, in wildfire management, it is helpful to find the distance of all points in an area from the wildfire’s boundary. Computing a distance transform on traditional Geographic Information Systems (GIS) is usually adopted from image processing methods, albeit prone to distortion resulting from flat maps. Discrete Global Grid Systems (DGGS) are relatively new low-distortion globe-based GIS that discretize the Earth into highly regular cells using multiresolution grids. In this paper, we introduce an efficient distance transform algorithm for DGGS. Our novel algorithm heavily exploits the hierarchy of a DGGS and its mathematical properties and applies to many different DGGSs. We evaluate our method by comparing its speed and distortion with the distance transform methods used in traditional GIS and general 3D meshes. We demonstrate that our method is efficient and has minimal distortion.

When predicting thunderstorms and localized severe weather events, close calls occur more frequently than direct hits. This makes it difficult for traditional verification approaches to fully represent forecast performance since events observed near a forecast event are counted both as misses and false alarms. Timing and location relative to the affected population are therefore two of the most important aspects of such a forecast. Verification of these aspects allows the determination of a safe distance for the user of a given severe weather alert. In this study, we propose a forecast verification measure based on the Generalized Distance Transform that is mathematically rigorous yet intuitive and user-friendly in its interpretation. The proposed measure compares the distance from a user location to an alert area against the distance from the same user location to a set of observed events. Time series for such comparisons can then be constructed, allowing evaluation of the timing error obtained from the difference between the two time series. Finally, the ‘worst overforecast’ and ‘worst underforecast’ are diagnosed in terms of relative distance.

A novel variational problem for approximating the distance function (to a domain boundary) is proposed. It is shown that this problem can be efficiently solved by ADMM. A review of several other variational and PDE-based methods for distance function estimation is presented. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments. Applications of the method to the problems of surface curvature estimation and computing the skeleton of a binary image are shown. [ABSTRACT FROM AUTHOR]

• The neighbourhood in an n -space is decomposed into neighbourhoods in (n − 1) -space. • Morphological operations in an n -space is the union of those on lines. • The object boundary is constructed from those in lower dimensional space. • The distance transform is computed from those in lower-dimensional space. We prove that the 2 n -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. [ABSTRACT FROM AUTHOR]

Distance transforms (DTs) are standard tools in image analysis, with applications in image registration and segmentation. The DT is based on extremal (minimal) distance values and is therefore highly sensitive to noise. We present a stochastic distance transform (SDT) based on discrete random sets, in which a model of element-wise probability is utilized and the SDT is computed as the first moment of the distance distribution to the random set. We present two methods for computing the SDT and analyze them w.r.t. accuracy and complexity. Further, we propose a method, utilizing kernel density estimation, for estimating probability functions and associated random sets to use with the SDT. We evaluate the accuracy of the SDT and the proposed framework on images of thin line structures and disks corrupted by salt and pepper noise and observe excellent performance. We also insert the SDT into a segmentation framework and apply it to overlapping objects, where it provides substantially improved performance over previous methods. Finally, we evaluate the SDT and observe very good performance, on simulated images from localization microscopy, a state-of-the-art super-resolution microscopy technique which yields highly spatially localized but noisy point-clouds. [ABSTRACT FROM AUTHOR]

Mobile robot carrying gas sensors have been widely used in mobile olfaction applications. One of the challenging tasks in this research field is Gas Distribution Mapping (GDM). GDM is a representation of how volatile organic compound is spatially dispersed within an environment. This paper addresses the effect of obstacles towards GDM for indoor environment. This work proposes a solution by improvising the Kernel DM + V technique using propagated distance transform (DT) as the weighing function. Since DT computations are CPU heavy, parallel computing, using Compute Unified Device Architecture (CUDA) available in Graphics Processing Unit (GPU), is used to accelerate the DT computation. The proposed solution is compared with the Kernel DM + V algorithm, presenting that the proposed method drastically improves the quality of GDM under various kernel sizes. The study is also further extended towards the effect of obstacles on gas source localization task. The outcome of this work proves that the proposed method shows better accuracy for GDM estimation and gas source localization if obstacle information is considered. [ABSTRACT FROM AUTHOR]

Recent research on spatial and spatio-temporal model checking provides novel image analysis methodologies, rooted in logical methods for topological spaces. Medical imaging (MI) is a field where such methods show potential for ground-breaking innovation. Our starting point is SLCS, the Spatial Logic for Closure Spaces—closure spaces being a generalisation of topological spaces, covering also discrete space structures—and topochecker, a model checker for SLCS (and extensions thereof). We introduce the logical language ImgQL ("Image Query Language"). ImgQL extends SLCS with logical operators describing distance and region similarity. The spatio-temporal model checker topochecker is correspondingly enhanced with state-of-the-art algorithms, borrowed from computational image processing, for efficient implementation of distance-based operators, namely distance transforms. Similarity between regions is defined by means of a statistical similarity operator, based on notions from statistical texture analysis. We illustrate our approach by means of an example of analysis of Magnetic Resonance images: segmentation of glioblastoma and its oedema. [ABSTRACT FROM AUTHOR]