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Background: The supporting quadric method(SQM) is a versatile method for designing freeform optics for desired irradiance redistribution, but the time of solution optimization increases rapidly with the refinement of the mapping grid. Objective: As the complexity of light distribution is getting higher and higher, time consumed will also increase exponentially. This paper proposes an idea of applying the deep neural network method to optical design. Methods: In this article, we established a special corresponding relationship and prepared a dataset, which underwent deep network learning and training. Finally, a hybrid design method of deep learning and optical design was realized and verified. Results: Compared with the traditional method, this method is more efficient. Here, we used a deep neural network(DNN) to accelerate the freeform optical design. After the DNN was trained by a sample set consisting of a uniform pattern and eight different Chinese characters represented by an array with 11 × 11, it can generate a character's reflector within few milliseconds. Conclusion: As proof of this new method, a character pattern reflector was manufactured and tested, and the experimental irradiance distribution was found close to the expectation, which means that the neural network has the excellent capability to memorize all of the learned characters. SQM combined with DNN has the potential to establish a particular “optical font library” and even offers a promising path for rapid freeform optical design to realize the function of “optical typography”.

This paper is concerned with the problem of multi-view 3D reconstruction with an un-calibrated micro-lens array based light field camera. To acquire 3D Euclidean reconstruction, existing approaches commonly apply the calibration with a checkerboard and motion estimation from static scenes in two steps. Self-calibration is the process of simultaneously estimating intrinsic and extrinsic parameters directly from un-calibrated light fields without the help of a checkerboard. While the self-calibration technique for conventional (pinhole) camera is well understood, how to extend it to light field camera remains a challenging task. This is primarily due to the ultra-small baseline of the light field camera. We propose an effective self-calibration method for a light field camera for automatic metric reconstruction without a laborious pre-calibration process. In contrast to conventional self-calibration, we show how such a self-calibration method can be made numerically stable, by exploiting the regularity and measurement redundancies unique for the light field camera. The proposed method is built upon the derivation of a novel ray-space homography constraint (RSHC) using Plucker parameterization as well as a ray-space infinity homography (RSIH). We also propose a new concept of “rays of the absolute conic (RAC)” defined as a special quadric in 5D projective space $${\mathbb {P}}^5$$ . A set of new equations are established and solved for self-calibration and 3D metric reconstruction specifically designed for a light field camera . We validate the efficacy of the proposed method on both synthetic and real light fields, and have obtained superior results in both accuracy and robustness.

Herein, we present a novel approach for monocular dual quadric initialization that combines three-dimensional (3D) map points with two-dimensional (2D) object detection for forward-translating camera movements. The traditional approach using 2D detection bounding boxes in multiple views fails in straight vehicle motion scenarios as object observation is limited to few frames. Although single image initialization is possible when multiple constraints are introduced, such initialization is based on strong assumptions. In this letter, we incorporate constraints from 3D map points with single-view 2D object detection to robustly initialize the dual quadric. Constraints from 3D map points are converted to planar constraints from their convex hull. Together with the projective planar constraints from bounding boxes, the proposed method can infer accurate dual quadric parameters. Further, comparison studies with the state of the art (SOTA) show that the proposed approach achieves the same accuracy of center localization but outperforms the existing methods in shape estimation and success ratio of initialization. The proposed method dose not rely on assumptions of dimension and pose of 3D objects; hence, it is more generic and accurate. Based on the KITTI raw dataset, the initialization success ratio is up to 97.7% with an average position error of 1.58 m, and 2D IoU of 80% when the number of map points per object accumulates to 60. When applied to the TUM RGB-D dataset, the proposed approach yields an initialization success ratio of 92.7% when the number of map points per object accumulates to 30, revealing a 16.2% increment compared with the SOTA using an RGB-D camera. Finally, we integrate the initialization method into a simultaneous localization and mapping system.

3D object detection is an essential component of scene perception and motion prediction in autonomous driving. Previous methods represent objects as the truncated signed distance fields (3D bounding box), which can only provide the geometric constraints of point-to-line. In this work, we define the object as a more compact representation, quadric (ellipsoid) in a 3D scene and a conic (ellipse) in an image, which can provide stronger geometric constraints of surface-to-curve. Specifically, we estimate a ellipsoid from a conic fitted by a 2D bounding box to obtain 3D object localization and occupancy. We further to formulate this constraint relation as a nonlinear optimization problem in dual space, which enables us to easy recover stable and accurate 3D object parameters by adding only three additional direction-aware branches to the existing 2D detection networks. In addition, we decouple the dimensions of object and update the length and orientation of objects in our iterative algorithm when the estimations from the 2D detection networks have different deviations. The final detection results can be obtained after passing through our geometry-related refinement network. We evaluate our method on the KITTI object detection benchmark and achieve the best performance among published monocular competitors.

We consider the problem of calculating a refractive element with two surfaces, forming a flat front and a given distribution of illumination. The supporting quadrics method is formulated for calculating a given optical element and it is shown that this method coincides with the gradient method for some functional related to the problem of the Monge-Kantorovich mass transfer problem. This enables adaptive selection of the step in the supporting quadric method. At the end of the article a design example is given.

Images of a nearby celestial body collected by a camera on an exploration spacecraft contain a wealth of actionable information. This work considers how the apparent location of the observed body's horizon in a digital image may be used to infer the relative position, attitude, or both. When the celestial body is a sphere, spheroid, or ellipsoid (as is the case for most large bodies in the Solar System), the projected horizon in an image is a conic-usually an ellipse at large distances and a hyperbola at small distances. This work develops non-iterative and analytically exact methods for every case (all combinations of unknown state parameters and quadric shapes), completely superseding older horizon-based methods that are iterative, approximate, or both. Some of the analytic methods presented in this work are new. Recognizing that these developments build on techniques that may be unfamiliar to many spacecraft navigators, this work is fashioned as a tutorial. Descriptive illustrations and numerical examples are provided to make concepts clear and to validate the proposed algorithms.

This paper considers a feedback control law that achieves attitude stabilization for Earth-pointing spacecraft using only magnetorquers as torque actuators. The control law is proportional derivative (PD)-like with matrix gains, and it guarantees asymptotic stability. The PD matrix gains are determined through the numerical solution of a periodic linear quadric regulator problem. A case study shows the effectiveness of the considered control law, and specifically of the gain selection method, in a simplified simulation scenario.

This study aimed to evaluate the influence of hamstrings and quadriceps strength on the hamstrings-to-quadriceps conventional (H:Qcon) and functional (H:Qfun) ratios in male soccer players. Quadric...

We present a novel and effective method for detecting 3D primitives in cluttered, unorganized point clouds, without axillary segmentation or type specification. We consider the quadric surfaces for encapsulating the basic building blocks of our environments - planes, spheres, ellipsoids, cones or cylinders, in a unified fashion. Moreover, quadrics allow us to model higher degree of freedom shapes, such as hyperboloids or paraboloids that could be used in non-rigid settings. We begin by contributing two novel quadric fits targeting 3D point sets that are endowed with tangent space information. Based upon the idea of aligning the quadric gradients with the surface normals, our first formulation is exact and requires as low as four oriented points. The second fit approximates the first, and reduces the computational effort. We theoretically analyze these fits with rigor, and give algebraic and geometric arguments. Next, by re-parameterizing the solution, we devise a new local Hough voting scheme on the null-space coefficients that is combined with RANSAC, reducing the complexity from $O(N^4)$ to $O(N^3)$ (three points). To the best of our knowledge, this is the first method capable of performing a generic cross-type multi-object primitive detection in difficult scenes without segmentation. Our extensive qualitative and quantitative results show that our method is efficient and flexible, as well as being accurate., Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI). arXiv admin note: substantial text overlap with arXiv:1803.07191

We propose a method for designing a refractive optical element with two working surfaces transforming an incident beam with a plane wavefront into an output beam with prescribed irradiance distribution and a non-planar wavefront. The presented method generalizes the supporting quadric method [Opt. Express 28, 22642 (2020)10.1364/OE.398990] proposed for collimated beam shaping to the case of a non-planar output wavefront. The method is simple to implement and is based on just a few main equations. We present several examples of designing optical elements (including elements with piecewise-smooth optical surfaces) generating light beams with prescribed irradiance distributions and wavefronts (spherical and aspherical). The examples demonstrate high performance of the method.

Conventional SLAM systems lack the ability to create semantically meaningful maps for scene understanding of robots. In this paper, we estimate a quadric surface for each object by detecting objects from different views and propose an object SLAM that uses dual quadric representations as 3D landmarks to overcome this limitation. A dual quadric can represent the position, orientation, size of an object compactly. We devise a geometric ellipse measurement model that addresses the problem of reconstructed object projection, and demonstrate how to integrate it into the SLAM system in order to jointly estimate camera poses and constrained dual quadric parameters. Our method is valuated on the public dataset. Experiments show the validity of creating maps with high-level information.

A new fractional two-dimensional quadric polynomial discrete chaotic map (2D-QPDM) with the discrete fractional difference is proposed. Afterwards, the new dynamical behaviors are observed, so that the bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits of the proposed map are given, respectively. The new discrete fractional map is exploited into color image encryption algorithm and it is illustrated with several examples. The proposed image encryption algorithm is analyzed in six aspects which indicates that the proposed algorithm is superior to other known algorithms as a conclusion.

Recent works on semantic Simultaneous Localization and Mapping (SLAM) utilizing object landmarks have shown superiority in terms of robustness and accuracy in tracking and localization. 3D object landmarks represented by a cubic or quadric surface are inferred from 2D object bounding boxes which are typically captured from multiple views by an object detector. Nevertheless, bounding box noises and small camera baseline may lead to an inaccurate 3D object landmark inference. Inspired by the dual quadric enveloping property, in this work, we introduce the horizontal support assumption to constrain rotation w.r.t. roll and pitch for a quadric representation. As the result, we reduce the number of quadric parameters and narrow down the solution space, and ultimately produce a relatively accurate inference. Extensive experimental evaluations under both simulated and real scenarios are conducted in this paper. Quantitative results demonstrate that our approach outperforms the state-of-the-art.

Simultaneous localization and mapping (SLAM) is a well-known problem in robotic applications. Many solutions consist in using handcrafted features as landmarks such as SIFT, SURF, ORB… These features are usually edges or corners which are invariant to some specific transformations. However, because of their low-level nature, they are not only non-informative but also not robust under various conditions (lightning, weather, point-of-view) and their track is often lost from one frame to another. To tackle this issue, the main idea of this work is to detect and localize higher-level landmarks such as static semantic objects instead. This paper focuses on the integration of circular traffic signs landmarks into a complete Extended Kalman Filter SLAM framework. The main part of this work consists in the quadric parametrization of the observation function and its inclusion in the Bayesian approach.

Visual Simultaneous localization and mapping (vS-LAM) are estimation problems in which a vehicle is localizing itself while reconstructing a map of the environment. Such approaches are usually solved using handcrafted 2D features resulting as simple geometrical shape landmarks. The main problems of such features are: (1) they are not robust enough and (2) are often lost or incorrectly matched over consecutive frames and (3) they do not carry any semantic information. In this paper, we propose to consider higher level semantic objects as landmarks. We focus on Traffic Signs that are excellent candidates for this role: they have a simple geometrical shape, can be easily detected and carry a strong semantic information. We propose to include such new high level landmarks into an EKF-SLAM framework. For this purpose, we developed an efficient way to estimate the 7 degrees of freedom of polygonal and circular traffic signs from a single stereo-vision observation to initialize such landmarks in a very accurate way so it can be easily used in the EKF based estimation process.

Indoor service robots need to build an object-centric semantic map to understand and execute human instructions. Conventional visual simultaneous localization and mapping (SLAM) systems build a map using geometric features such as points, lines, and planes as landmarks. However, they lack a semantic understanding of the environment. This paper proposes an object-level semantic SLAM algorithm based on RGB-D data, which uses a quadric surface as an object model to compactly represent the object&rsquo, s position, orientation, and shape. This paper proposes and derives two types of RGB-D camera-quadric observation models: a complete model and a partial model. The complete model combines object detection and point cloud data to estimate a complete ellipsoid in a single RGB-D frame. The partial model is activated when the depth data is severely missing because of illuminations or occlusions, which uses bounding boxes from object detection to constrain objects. Compared with the state-of-the-art quadric SLAM algorithms that use a monocular observation model, the RGB-D observation model reduces the requirements of the observation number and viewing angle changes, which helps improve the accuracy and robustness. This paper introduces a nonparametric pose graph to solve data associations in the back end, and innovatively applies it to the quadric surface model. We thoroughly evaluated the algorithm on two public datasets and an author-collected mobile robot dataset in a home-like environment. We obtained obvious improvements on the localization accuracy and mapping effects compared with two state-of-the-art object SLAM algorithms.

We propose a version of the supporting quadric method for calculating a refractive optical element with two working surfaces for collimated beam shaping. Using optimal mass transportation theory and generalized Voronoi cells, we show that the proposed method can be regarded as a gradient method of maximizing a concave function, which is a discrete analogue of the Lagrange functional in the corresponding mass transportation problem. It is demonstrated that any maximum of this function provides a solution to the problem of collimated beam shaping. Therefore, the proposed method does not suffer from “trapping” at a local extremum, which is typical for gradient methods. We present design examples of refractive optical elements illustrating high performance of the method.

A main challenge for today’s renderers is the ever-growing size of 3D scenes, exceeding the capacity of typically available main memory. This especially holds true for graphics processing units (GPUs) which could otherwise be used to greatly reduce rendering time. A lot of the memory is spent on detailed geometry with mostly imperceptible influence on the final image, even in a global illumination context. Illumination-driven mesh reduction, a Monte Carlo–based global illumination simulation, steers its mesh reduction towards areas with low visible contribution. While this works well for preserving high-energy light paths such as caustics, it does have problems: First, objects casting shadows while not being visible themselves are not preserved, resulting in highly inaccurate shadows. Secondly, non-transparent objects lack proper reduction guidance since there is no importance gradient on their backside, resulting in visible over-simplification. We present a solution to these problems by extending illumination-driven mesh reduction with occluder information, focusing on their silhouettes as well as combining it with commonly used error quadrics to preserve geometric features. Additionally, we demonstrate that the combined algorithm still supports iterative refinement of initially reduced geometry, resulting in an image visually similar to an unreduced rendering and enabling out-of-core operation.

With the rapid development of drone technology and digital camera technology, the method of obtaining high-precision coordinates based on UAV aerial photogrammetry technology is popular. The plane coordinate accuracy of the aerial image of the drone has been able to meet the needs of practical applications, but the elevation accuracy is generally low. Aiming at the low elevation accuracy of UAV aerial photogrammetry, a multi-face function fitting method based on Vondrak filter optimization was proposed. The improved fitting model was used to obtain the elevation correction value of the aerial image, thereby obtaining high-precision image elevation data. In this paper, based on the traditional multi-face function fitting method, some known points were used to model and find the difference between the measured elevation value and the measured elevation. The Vondrak filter was used to smooth the fitting result. Finally, a small number of known elevation points were used for checking, so that the obtained elevation was compared with the actual elevation. The experimental comparison showed that the improved multi-face function fitting method used Vondrak filter was improved by 34.76% compared with the quadric surface fitting, and improved by 14.48% compared with the optimized cubic surface fitting method. Research shows that the multi-faceted function method based on Vondrak filtering is superior to the traditional elevation correction method. The experiment verifies the effectiveness and feasibility of the improved method, and provides some reference value for the research of aerial image elevation correction model.

The laser beam with asymmetric divergence angle distribution generated by a laser diode (LD) terribly restricts its application in space laser communication. In this paper, an off-axis transmitting antenna with two parabolic cylindrical reflective mirrors is designed to simultaneously shape, collimate and transmit the laser beam. The simulation results demonstrated that the ratio of beam waist (RBW) of the output beam can be reduced from 2.9998 to 1.0003 and the maximum divergence angle of the output light is compressed to 3.98 μ rad. The performance of the system is evaluated under different astigmatism of LD and different transmitting distance. Compared with previous methods, the method proposed in this paper has three main advantages: non-dispersion, fewer reflective mirrors and processing convenience. This paper may not only provide engineers with more practical beam-shaping systems but also provided idea to the designers of off-axis system

We propose an approach for the three-dimensional solid reconstruction of a human bone using medical images obtained from Computed tomography (CT). CT images of the female from the Visible Korean (VK) data set, which were constructed in the VK human project, were used. First, the femur and hip bone images were segmented from the original image. The segmented images were then smoothed by a Gaussian filter, and a triangular mesh was generated using the marching-cubes algorithm. To reduce the triangles in the generated mesh and eliminate aliasing, a triangle decimation algorithm using the quadric error metric method was adopted. To reconstruct the surfaces, the triangles in the mesh were interpolated with cubic triangular Bezier patches. The patches were then converted to a solid by stitching them. Finally, it is demonstrated that the proposed approach can be used in a practical design environment by importing the reconstructed solids into a commercial computer-aided design software.

In this chapter, we review methods for representing, storing and processing 3D data. We focus in particular on representations for raw 3D data, surface-based and solid-based models. We describe and compare various data structures available for representing triangular meshes and formats for mesh storage. We also provide details on three different subdivision schemes and explain how differential surface properties can be computed from different surface representations. In the context of data compression, we describe in detail the Quadric Error Metric algorithm for mesh simplification. Finally, we suggest areas for future work in this area and provide some concluding remarks.

With the development of 3D scanning technology, a huge volume of point cloud data has been collected at a lower cost. The huge data set is the main burden during the data processing of point clouds, so point cloud simplification is critical. The main aim of point cloud simplification is to reduce data volume while preserving the data features. Therefore, this paper provides a new method for point cloud simplification, named FPPS (feature-preserved point cloud simplification). In FPPS, point cloud simplification entropy is defined, which quantifies features hidden in point clouds. According to simplification entropy, the key points including the majority of the geometric features are selected. Then, based on the natural quadric shape, we introduce a point cloud matching model (PCMM), by which the simplification rules are set. Additionally, the similarity between PCMM and the neighbors of the key points is measured by the shape operator. This represents the criteria for the adaptive simplification parameters in FPPS. Finally, the experiment verifies the feasibility of FPPS and compares FPPS with other four-point cloud simplification algorithms. The results show that FPPS is superior to other simplification algorithms. In addition, FPPS can partially recognize noise.

Simultaneous Localization And Mapping (SLAM) is a fundamental problem in mobile robotics. While sparse point-based SLAM methods provide accurate camera localization, the generated maps lack semantic information. On the other hand, state of the art object detection methods provide rich information about entities present in the scene from a single image. This work incorporates a real-time deep-learned object detector to the monocular SLAM framework for representing generic objects as quadrics that permit detections to be seamlessly integrated while allowing the real-time performance. Finer reconstruction of an object, learned by a CNN network, is also incorporated and provides a shape prior for the quadric leading further refinement. To capture the dominant structure of the scene, additional planar landmarks are detected by a CNN-based plane detector and modeled as independent landmarks in the map. Extensive experiments support our proposed inclusion of semantic objects and planar structures directly in the bundle-adjustment of SLAM - Semantic SLAM - that enriches the reconstructed map semantically, while significantly improving the camera localization. The performance of our SLAM system is demonstrated in https://youtu.be/UMWXd4sHONw and https://youtu.be/QPQqVrvP0dE ., Accepted to ICRA 2019 (for video demo look at https://youtu.be/UMWXd4sHONw and https://youtu.be/QPQqVrvP0dE)

The demand for indoor localization is becoming urgent, but the traditional location fingerprint approach takes a lot of manpower and time to construct a fine-grained location fingerprint database. To address this problem, we propose to use the approach of combining dynamic collection of fingerprint samples with Radial Basis Function (RBF) interpolation. Specifically, the raw sparse fingerprint database is constructed from a small number of fingerprints collected on a few paths, in which the pedestrian track correction algorithm improves the validity and accuracy of the sparse fingerprint database. Then, the RBF interpolation approach is applied to enrich the sparse fingerprint database, in which the Genetic Algorithm (GA) is used to optimize the free shape parameter and the cut-off radius is determined according to the experimental results. Extensive experiments show that the proposed approach guarantees high interpolation and localization accuracy and also significantly reduces the effort of manual collection of fingerprint samples.

As a preprocessing step for computer vision tasks, research on generating superpixels of an image has been widely conducted recently. In this paper, we propose a fully automatic superpixel generation algorithm by simplifying the 3D triangle mesh modeled from a 2D input image. The simplification is performed based on a modified quadric error metric (QEM) method. The pipeline of our algorithm is simple. Given an image, we first turn it into a 2D triangle mesh and then lift the mesh to 3D based on the gray values of the image. We then simplify the 3D mesh based on the modified QEM method which encodes the features in the image intrinsically to ensure feature-aware superpixels. After obtaining the simplified mesh, we map it back to the 2D image to generate triangular-shaped superpixels. Our algorithm is fully automatic. The number of superpixels can be controlled intuitively. Experimental results demonstrate the effectiveness of our approach.

This paper presents a region-based method for extraction of consistent surfaces from raw point clouds. The method uses a new robust estimation method of constructing seed regions and a new method of orientating regions or surfaces. The robust estimation method selects good seed regions from candidate regions generated randomly in a structured neighborhood. The orientation method uses transition vectors from which include angles of adjacent normal vectors are not greater than 90° and thus can be orientated correctly crossing sharp features or close-by opposite surfaces. The region-based method consists of two levels of segmentation: planar segmentation and quadric segmentation, both of which produce consistent surfaces. The quadric segmentation fits general quadrics by 3 L fitting algorithm in its region growing process and can take consistent planar surfaces as initials. Experimental results show that the robust estimation method has higher probability of success than the traditional one and the orientation method works well. Experimental results also demonstrate the applicability of our method to various data.

Quadrics are a compact mathematical formulation for a range of primitive surfaces. A problem arises when there are not enough data points to compute the model but knowledge of the shape is available. This paper presents a method for fitting a quadric with a Bayesian prior. We use a matrix normal prior in order to favour ellipsoids when fitting to ambiguous data. The results show the algorithm copes well when there are few points in the point cloud, competing with contemporary techniques in the area.

Modern architecture of civil engineering structures made of reinforced concrete is demanding solutions to problems related to design and construction of roofs shaped as creative forms which require an adequate combination of arts and physical-mathematical models. In that sense, the quadric and cylindrical surfaces offer an attractive based on their volumetric expression, historicity, and mathematical feasibility. In this work, seven cylindrical and quadric surfaces named elliptic cylinder, parabolic cylinder, elliptic cone, elliptic paraboloid, hyperbolic paraboloid, ellipsoid and hyperboloid of two sheets have been analysed to find out which of them show to be more efficient when used as reinforced concrete roof structures. To do so, the configuration of each structure hase been adjusted in terms of similar stiffness, strength parameters and enclosed volume. The structural efficiency was computed using the results of weight/load ratio, available strength, material consumption and relative stiffness. The solution of the model has been achieved using a combination of exact solutions and numerical methods. To compute the model results a Matlab® code was written and validated using the structural software SAP2000®. The best structural efficiency in terms of stiffness, strength, and materials consumption was obtained for roofs configurated using surfaces built from parabolas, i.e., elliptic paraboloid, hyperbolic paraboloid, and parabolic cylinder. The results of this work can be used in future studies and applications related to arhitectural comfort, structural behaviour and material consumption in construction of roofs.

In order to improve the accuracy of image edge detection, this paper studies the adaptive image edge detection technology based on discrete algorithm and classical Canny operator. First, the traditional sub-pixel edge detection method is illustrated based on the related literature research. Then, Canny operator is used for detection, the edge model of the quadric curve is established using discrete data, and the adaptive image edge parameters are obtained using one-dimensional gray moment. Experimental results show that the accuracy of feature detection is 99%, which can be applied to the practice of image edge detection to a certain extent.

Redistribution of light from a given source in order to create a prescribed intensity pattern on a given set in 3D space is a task arising in numerous applications. Designing optical systems with capabilities to perform such tasks reliably in a wide variety of applications is the overall goal of much of research in optics. In many important practical cases the a priori requirement of radial symmetry should not be imposed neither on the input/output radiances nor on the geometry of the input/output beams. Such cases include the “laser beam shaping problem” requiring transformation of a Gaussian beam from a laser into a beam with “flat top” intensity profile and “picture” generation or creation of illumination patterns on flat, tilted and curved surfaces with non-uniform input/output distributions. In all such cases utilization of freeform optical surfaces is a must. The “Supporting Quadric Method (SQM) was developed to solve problems of this kind. It provides physically motivated and mathematically rigorous theoretical and computational tools for dealing with such design problems.

To address low efficiency of traditional fingerprint database construction approach, we propose a fingerprint database expansion approach based on Multiquadric Radial Basis Function (RBF) interpolation. First of all, multi-directional fingerprints are collected dynamically, and sparse fingerprint database is generated by combining Received Signal Strength (RSS) and coordinates. Subsequently, RSS of each new Reference Point (RP) is estimated by using optimized RBF approach. In particular, Genetic Algorithm (GA) is applied to optimize shape parameter, so as to improve interpolation accuracy. Extensive experimental results show that the proposed approach is able to achieve high localization accuracy as well as significantly reduce fingerprint database construction effort.

Freeform optics constitutes a new technology that is currently driving substantial changes in illumination design. It liberates designers and engineers from restrictions of optical surface geometry, enabling them to achieve compact, lightweight, and efficient illumination systems with excellent optical performance. Freeform optics is currently used widely for both fundamental research and practical applications. This Review focuses on the design of freeform illumination optics, which is a key factor in advancing the development of illumination engineering. The design methods of freeform illumination optics can be divided into two groups: zero-´etendue algorithms based on ideal source assumption and design algorithms for extended light sources. The zero-´etendue algorithms include ray mapping method, Monge–Ampère equation method, and supporting quadric method. The algorithms for extended sources include illumination optimization, feedback design, and simultaneous multiple surfaces method. The characteristics and limitations of these design methods are illustrated and a summary of these methods with future outlooks is also given.

This paper proposes a segmentation-free, automatic and efficient procedure to detect general geometric quadric forms in point clouds, where clutter and occlusions are inevitable. Our everyday world is dominated by man-made objects which are designed using 3D primitives (such as planes, cones, spheres, cylinders, etc.). These objects are also omnipresent in industrial environments. This gives rise to the possibility of abstracting 3D scenes through primitives, thereby positions these geometric forms as an integral part of perception and high level 3D scene understanding. As opposed to state-of-the-art, where a tailored algorithm treats each primitive type separately, we propose to encapsulate all types in a single robust detection procedure. At the center of our approach lies a closed form 3D quadric fit, operating in both primal & dual spaces and requiring as low as 4 oriented-points. Around this fit, we design a novel, local null-space voting strategy to reduce the 4-point case to 3. Voting is coupled with the famous RANSAC and makes our algorithm orders of magnitude faster than its conventional counterparts. This is the first method capable of performing a generic cross-type multi-object primitive detection in difficult scenes. Results on synthetic and real datasets support the validity of our method., Accepted for publication at CVPR 2018

Research in Simultaneous Localization And Mapping (SLAM) is increasingly moving towards richer world representations involving objects and high level features that enable a semantic model of the world for robots, potentially leading to a more meaningful set of robot-world interactions. Many of these advances are grounded in state-of-the-art computer vision techniques primarily developed in the context of image-based benchmark datasets, leaving several challenges to be addressed in adapting them for use in robotics. In this paper, we derive a SLAM formulation that uses dual quadrics as 3D landmark representations, exploiting their ability to compactly represent the size, position and orientation of an object, and show how 2D bounding boxes (such as those typically obtained from visual object detection systems) can directly constrain the quadric parameters via a novel geometric error formulation. We develop a sensor model for deep-learned object detectors that addresses the challenge of partial object detections often encountered in robotics applications, and demonstrate how to jointly estimate the camera pose and constrained dual quadric parameters in factor graph based SLAM with a general perspective camera.

In this paper, we use 2D object detections from multiple views to simultaneously estimate a 3D quadric surface for each object and localize the camera position. We derive a SLAM formulation that uses dual quadrics as 3D landmark representations, exploiting their ability to compactly represent the size, position and orientation of an object, and show how 2D object detections can directly constrain the quadric parameters via a novel geometric error formulation. We develop a sensor model for object detectors that addresses the challenge of partially visible objects, and demonstrate how to jointly estimate the camera pose and constrained dual quadric parameters in factor graph based SLAM with a general perspective camera., Accepted at IEEE Robotics and Automation Letters (RA-L). arXiv admin note: text overlap with arXiv:1708.00965

We report what to our knowledge is the first theoretical prediction of the coupling efficiency of a laser diode emitting two wavelengths either 1.3 or 1.5 μm, to three elliptic core step index fibers with different aspect ratios via quadric interface microlens of three different focal lengths on the fiber tip. Here, quadric interface microlens contains elliptical (hemispherical included), hyperbolic and parabolic microlenses. Instead of considering special ABCD matrix for individual microlens, a simple, accurate, and popular unified transfer ABCD matrix for refraction of quadric microlens under paraxial approximation is utilized to analyze the theoretical coupling efficiency, based on Gaussian beam approximation. The coupling efficiency can reach as high as 98.63 % with optimizing structure parameters of specific lensed fiber. The analysis can give some guidance for fabricating quadric interface lensed elliptic core fiber which are mainly useful in polarisation-maintaining fiber optic sensors and coherent fiber optic communication systems.

Las técnicas de remallado buscan modificar la malla de entrada para adaptarla a la aplicación específica. En este trabajo se propone una metodología de remallado especializada en el rostro humano, cuyo propósito es reducir el número de caras y vértices que requiere la malla, manteniendo las características propias de la anatomía humana. Para lograr esto se utiliza la información de curvatura, la cual destaca la anisotropía intrínseca en la geometría natural o en la geometría de origen humano. Como resultado se obtuvieron mallas anisotrópicas poligonales, compuestas principalmente por cuadriláteros, con menos del 50% de los puntos y caras de la malla inicial, que mantienen las características anatómicas para modelos del rostro en expresión neutra, o con expresiones de alegría, enojo, repugnancia, miedo, sorpresa y tristeza. La metodología se validó con los modelos presentes en la base de datos BU-3DFE, y se comparó la calidad de los resultados obtenidos contra el remallado que se logra con la técnica de simplificación basada en quadric error metrics

In this article, we investigate the use of joint �-entropy for 3D ear matching by incorporating the local shape feature of 3D ears into the joint �-entropy. First, we extract a sufficient number of key points f rom the 3D ear point cloud, and fit the neighborhood of each key point to a single-value quadric surface on product parameter regions. Second, we define the local shape feature vector of each key point as the sampling depth set on the parametric node of the quadric surface. Third, for every pair of gallery ear and probe ear, we construct the minimum spanning tree (MST) on their matched key points. Finally, we minimize the total edge weight of MST to estimate its joint �-entropy — the smaller the entropy is, the more similar the ear pair is. We present several examples to demonstrate the advantages of our algorithm, including low time complexity, high recognition rate, and high robustness. To the best of our knowledge, it is the first time that, in computer graphics, the classical information theory of joint �-entropy is used to deal with 3D ear shape recognition.

A new method is proposed for testing standard quadric surfaces with several subapertures based on interferometry. Subapertures arrangement, best-fit sphere calculation and distortion correction about such surfaces are discussed in this paper. In addition, we provide an experimental demonstration by testing a O310 mm convex hyperboloid mirror. The experimental result shows that the proposed method can accomplish the testing of quadric mirrors without auxiliary compensation effectively. The analysis and proposed methods bring much to the application of non-null aspheric testing.

The adaptation of bones to mechanical loads or bone remodeling can be simulated using specific mathematical models in conjunction with the finite element method. There are several theories proposed within the literature for the prediction of the bone behavior under mechanical loads and all have been used successfully, within certain limits of prediction details, but no unanimous acceptance have been reported yet. Within this context, it is important to know the differences and similarities between the results which these theories can produce, in order to improve their interpretation. On the basics of the above observation, the paper presents the comparison between density distributions achieved using three different models of bone remodeling: the original strain energy density equation developed at the University of Nijmegen, the principle of cellular accommodation incorporated into the Nijmegen model and the variant developed at the University of Manchester obtained by adding the quadric term which eliminates the density accumulation at physiologically unrealistic high loads. It is shown, using a suggestive test problem, that the three models generate significantly different results.

International audience; The specularity prediction task in images, given the camera pose and scene geometry, is challenging and ill-posed. A recent approach called JOint LIght-MAterial Specularity (JOLIMAS) addresses this problem using a geometric model under the assumption that specularities have an elliptical shape. We address the most recent version of the model, Dual JOLIMAS, which is limited to planar and convex surfaces where the local surface's curvature under the specularity is constant. We propose a canonical representation of the JOLIMAS model that is independent of the local surface curvature. To reconstruct our model represented by a 3D quadric, we use at least 3 ellipses fitted to specularities and transform their shape to fit a planar surface and simulate a planar mirror which does not distort the image of the reflected object. After reconstruction, we project the 3D quadric into an ellipse and transform it to fit the current local curvature of the surface on a new viewpoint. We assessed this method on both synthetic and real sequences, and compared it to the previous approach Dual JOLIMAS.

Predicting specularities in images, given the camera pose and scene geometry from SLAM, forms a challenging and open problem. It is nonetheless essential in several applications such as retexturing. A recent geometric model called JOLIMAS partially answers this problem, under the assumptions that the specularities are elliptical and the scene is planar. JOLIMAS models a moving specularity as the image of a fixed 3D quadric. We propose dual JOLIMAS, a new model which raises the planarity assumption. It uses the fact that specularities remain elliptical on convex surfaces and that every surface can be divided in convex parts. The geometry of dual JOLIMAS then uses a 3D quadric per convex surface part and light source, and predicts the specularities by a means of virtual cameras, allowing it to cope with surface's unflatness. We assessed the efficiency and precision of dual JOLIMAS on multiple synthetic and real videos with various objects and lighting conditions. We give results of a retexturing application. Further results are presented as supplementary video material.

Electromagnetic tracking (EMT) systems are often used to track the position and orientation of a navigation tool during navigated surgery operations. But, their sensitivity to field distortions originating from electromagnetic emitting devices or metallic objects present in the environment reduces measurement accuracy. The purpose of this study is to incorporate orientation information in correcting position data provided by EMT based on Hardy's Multi-Quadric method (HMQ). We implemented the HMQ algorithm in two ways: the basic form in which location data is used only and the modified form in which both the orientation and location data are incorporated into a normalized vector in the relevant formula. Comparing the corrected position data with their corresponding reference values, which are provided by the optical tracking system, it is observed that the mean global error is reduced approximately by half and the variance is decreased nearly to its one tenth.

Time-varying, smooth trajectory estimation is of great interest to the vision community for accurate and well behaving 3D systems. In this paper, we propose a novel principal component local regression filter acting directly on the Riemannian manifold of unit dual quaternions $\mathbb{D} \mathbb{H}_1$. We use a numerically stable Lie algebra of the dual quaternions together with $\exp$ and $\log$ operators to locally linearize the 6D pose space. Unlike state of the art path smoothing methods which either operate on $SO\left(3\right)$ of rotation matrices or the hypersphere $\mathbb{H}_1$ of quaternions, we treat the orientation and translation jointly on the dual quaternion quadric in the 7-dimensional real projective space $\mathbb{R}\mathbb{P}^7$. We provide an outlier-robust IRLS algorithm for generic pose filtering exploiting this manifold structure. Besides our theoretical analysis, our experiments on synthetic and real data show the practical advantages of the manifold aware filtering on pose tracking and smoothing.

This article proposes a new dual quaternion based approach for motion interpolation . The highlight is that dual quaternions act in the usual way on points, even if the Study condition is not fulfilled. This induces a fibration of kinematic image space into straight lines that describe the same rigid body displacement. This allows to use standard interpolation schemes for (piecewise) rational curves in a linear space rather than on the curved Study quadric.

Specularities are often problematic in computer vision since they impact the dynamic range of the image intensity. A natural approach would be to predict and discard them using computer graphics models. However, these models depend on parameters which are difficult to estimate (light sources, objects’ material properties and camera). We present a geometric model called JOLIMAS: JOint LIght-MAterial Specularity, which predicts the shape of specularities. JOLIMAS is reconstructed from images of specularities observed on a planar surface. It implicitly includes light and material properties, which are intrinsic to specularities. This model was motivated by the observation that specularities have a conic shape on planar surfaces. The conic shape is obtained by projecting a fixed quadric on the planar surface. JOLIMAS thus predicts the specularity using a simple geometric approach with static parameters (object material and light source shape). It is adapted to indoor light sources such as light bulbs and fluorescent lamps. The prediction has been tested on synthetic and real sequences. It works in a multi-light context by reconstructing a quadric for each light source with special cases such as lights being switched on or off. We also used specularity prediction for dynamic retexturing and obtained convincing rendering results. Further results are presented as supplementary video material, which can be found on the Computer Society Digital Library at http://doi.ieeecomputersociety.org/10.1109/TVCG.2017.2677445 .

Quadric surfaces are one of the geometric elements most commonly used for shape expression and mechanical accessory cartography in three dimensions. Since quadric surfaces cannot be represented exactly using polynomials, it is not suitable to deal with most problems encountered in engineering application. For this reason, we present a new method for polynomial approximation of quadric surfaces. The approximation tensor product surface obtained by the proposed method has no limit on its degree, i.e., arbitrary degree. It has C(k,h) (k,h=0,1,2) continuity at four corners with the original quadric surface. Meanwhile, the method has an optimal approximation result in the L2-norm, and it can also be applied to piecewise continuous quadric surface patches or a quadric surface patch combined with surface subdivision scheme. And the resulting piecewise approximation patches are globally C0 continuous. Finally, error estimation for the approximation method is given and numerical examples are presented to validate the feasibility and effectiveness of our method.

In order to meet the needs of wind speed prediction in wind farms, we consider the influence of random atmospheric disturbances on wind variations. Considering a simplified fluid convection mode, a Lorenz system can be employed as an atmospheric disturbance model. Here Lorenz disturbance is defined as the European norm of the solutions of the Lorenz equation. Grey generating and accumulated generating models are employed to explore the relationship between wind speed and its related disturbance series. We conclude that a linear or quadric polynomial generating model are optimal through the verification of short-term wind speed prediction in the Sotavento wind farm. The new proposed model not only greatly improves the precision of short-term wind speed prediction, but also has great significance for the maintenance and stability of wind power system operation.