The papers in this special section were presented at the Computer Vision and Pattern Recognition conference.

Symmetries and repetitions are common and valuable features in urban scenes. We propose to leverage such regularity information in an efficient optimization scheme in order to segment a rectified image of a facade into semantic categories. Our method retrieves a parsing which respects common architectural constraints as well as detected repetitive structures and edge information. Additionally, the use of symmetry information allows us to efficiently deal with large occluded areas and to recover plausible facade images with a minimum of occlusions. Our approach yields state-of-the-art accuracy on datasets with challenging occlusions. Competitive works either fully fail to deal with large occlusions or they are an order of magnitude slower than our approach.

Humans take advantage of real world symmetries for various tasks, yet capturing their superb symmetry perception mechanism with a computational model remains elusive. Motivated by a new study demonstrating the extremely high inter-person accuracy of human perceived symmetries in the wild, we have constructed the first deep-learning neural network for reflection and rotation symmetry detection (Sym-NET), trained onphotos from MS-COCO (Microsoft-Common Object in COntext) dataset with nearly 11K consistent symmetry-labels from more than 400 human observers. We employ novel methods to convert discrete human labels into symmetry heatmaps, capture symmetry densely in an image and quantitatively evaluate Sym-NET against multiple existing computer vision algorithms. On CVPR 2013 symmetry competition testsets and unseen MS-COCO photos, Sym-NET significantly outperforms all other competitors. Beyond mathematically well-defined symmetries on a plane, Sym-NET demonstrates abilities to identify viewpoint-varied 3D symmetries, partially occluded symmetrical objects, and symmetries at a semantic level.

This paper is a reaction to the poor performance of symmetry detection algorithms on real-world images, benchmarked since CVPR 2011. Our systematic study reveals significant difference between human labeled (reflection and rotation) symmetries on photos and the output of computer vision algorithms on the same photo set. We exploit this human-machine symmetry perception gap by proposing a novel symmetry-based Turing test. By leveraging a comprehensive user interface, we collected more than 78,000 symmetry labels from 400 Amazon Mechanical Turk raters on 1,200 photos from the Microsoft COCO dataset. Using a set of ground-truth symmetries automatically generated from noisy human labels, the effectiveness of our work is evidenced by a separate test where over 96% success rate is achieved. We demonstrate statistically significant outcomes for using symmetry perception as a powerful, alternative, image-based reCAPTCHA.

We present an approach for detecting and matching building facades between aerial view and street-view images. We exploit the regularity of urban scene facades as captured by their lattice structures and deduced from median-tiles' shape context, color, texture and spatial similarities. Our experimental results demonstrate effective matching of oblique and partially-occluded facades between aerial and ground views. Quantitative comparisons for automated urban scene facade matching from three cities show superior performance of our method over baseline SIFT, Root-SIFT and the more sophisticated Scale-Selective Self-Similarity and Binary Coherent Edge descriptors. We also illustrate regularity-based applications of occlusion removal from street views and higher-resolution texture-replacement in aerial views.

Dance is a dynamic art form that reflects a wide range of cultural diversity and individuality. With the advancement of motion-capture technology combined with crowd-sourcing and machine learning algorithms, we explore the complex relationship between perceived dance quality/dancer's gender and dance movements/music respectively. As a feasibility study, we construct a computational framework for an analysis-synthesis-feedback loop using a novel multimedia dance-music texture representation. Furthermore, we integrate crowd-sourcing, music and motion-capture data, and machine learning-based methods for dance segmentation, analysis and synthesis of new dancers. A quantitative validation of this framework on a motion-capture dataset of 172 dancers evaluated by more than 400 independent on-line raters demonstrates significant correlation between human perception and the algorithmically intended dance quality or gender of synthesized dancers. The technology illustrated in this work has a high potential to advance the multimedia entertainment industry via dancing with Turks.

We propose a novel regularity-driven framework for facade detection from aerial images of urban scenes. Gini-index is used in our work to form an edge-based regularity metric relating regularity and distribution sparsity. Facade regions are chosen so that these local regularities are maximized. We apply a greedy adaptive region expansion procedure for facade region detection and growing, followed by integer quadratic programming for removing overlapping facades to optimize facade coverage. Our algorithm can handle images that have wide viewing angles and contain more than 200 facades per image. The experimental results on images from three different cities (NYC, Rome, San-Francisco) demonstrate superior performance on facade detection in both accuracy and speed over state of the art methods. We also show an application of our facade detection for effective cross-view facade matching.

We employ hierarchical data association to track players in team sports. Player movements are often complex and highly correlated with both nearby and distant players. A single model would require many degrees of freedom to represent the full motion diversity and could be difficult to use in practice. Instead, we introduce a set of Game Context Features extracted from noisy detections to describe the current state of the match, such as how the players are spatially distributed. Our assumption is that players react to the current situation in only a finite number of ways. As a result, we are able to select an appropriate simplified affinity model for each player and time instant using a random decision forest based on current track and game context features. Our context-conditioned motion models implicitly incorporate complex inter-object correlations while remaining tractable. We demonstrate significant performance improvements over existing multi-target tracking algorithms on basketball and field hockey sequences several minutes in duration and containing 10 and 20 players respectively.

We propose a novel unsupervised method for discovering recurring patterns from a single view. A key contribution of our approach is the formulation and validation of a joint assignment optimization problem where multiple visual words and object instances of a potential recurring pattern are considered simultaneously. The optimization is achieved by a greedy randomized adaptive search procedure (GRASP) with moves specifically designed for fast convergence. We have quantified systematically the performance of our approach under stressed conditions of the input (missing features, geometric distortions). We demonstrate that our proposed algorithm outperforms state of the art methods for recurring pattern discovery on a diverse set of 400+ real world and synthesized test images.

We propose a novel approach for multi-camera autocalibration by observing multiview surveillance video of pedestrians walking through the scene. Unlike existing methods, we do NOT require tracking or explicit correspondences of the same person across time/views. Instead, we take noisy foreground blobs as the only input and rely on a joint optimization framework with robust statistics to achieve accurate calibration under challenging scenarios. First, each individual camera is roughly calibrated into its local World Coordinate System (lWCS) based on analysis of relative 3D pedestrian height distribution. Then, all lWCSs are iteratively registered with respect to a shared global World Coordinate System (gWCS) by incorporating robust matching with a partial Direct Linear Transform (pDLT). As demonstrated by extensive evaluation, our algorithm achieves satisfactory results in various camera settings with up to moderate crowd densities with a large proportion of foreground outliers.

We generalize the concept of bilateral reflection symmetry to curved glide-reflection symmetry in 2D euclidean space, such that classic reflection symmetry becomes one of its six special cases. We propose a local feature-based approach for curved glidereflection symmetry detection from real, unsegmented 2D images. Furthermore, we apply curved glide-reflection axis detection for curved reflection surface detection in 3D images. Our method discovers, groups, and connects statistically dominant local glidereflection axes in an Axis-Parameter-Space (APS) without preassumptions on the types of reflection symmetries. Quantitative evaluations and comparisons against state-of-the-art algorithms on a diverse 64-test-image set and 1,125 Swedish leaf-data images show a promising average detection rate of the proposed algorithm at 80 and 40 percent, respectively, and superior performance over existing reflection symmetry detection algorithms. Potential applications in computer vision, particularly biomedical imaging, include saliency detection from unsegmented images and quantification of deviations from normality. We make our 64-test-image set publicly available.

Time-varying spatial patterns are common, but few computational tools exist for discovering and tracking multiple, sometimes overlapping, spatial structures of targets. We propose a multi-target tracking framework that takes advantage of spatial patterns inside the targets even though the number, the form and the regularity of such patterns vary with time. RANSAC-based model fitting algorithms are developed to automatically recognize (or dismiss) (il)legitimate patterns. Patterns are represented using a mixture of Markov Random Fields (MRF) with constraints (local and global) and preferences encoded into pairwise potential functions. To handle pattern variations continuously, we introduce a posterior probability for each spatial pattern modeled as a Bernoulli distribution. Tracking is achieved by inferring the optimal state configurations of the targets using belief propagation on a mixture of MRFs. We have evaluated our formulation on real video data with multiple targets containing time-varying lattice patterns and/or reflection symmetry patterns. Experimental results of our proposed algorithm show superior tracking performance over existing methods.

We introduce a novel data-driven mean-shift belief propagation (DDMSBP) method for non-Gaussian MRFs, which often arise in computer vision applications. With the aid of scale space theory, optimization of non-Gaussian, multimodal MRF models using DDMSBP becomes less sensitive to local maxima. This is a significant improvement over standard BP inference, and extends the range of methods that are computationally tractable. In particular, when pair-wise potentials are Gaussians, the time complexity of DDMSBP becomes bilinear in the numbers of states and nodes in the MRF. Experimental results from simulation and non-rigid deformable neuroimage registration demonstrate that our method is faster and more accurate than state-of-the-art inference algorithms.

Increasingly, geographic information is being associated with personal photos. Recent research results have shown that the additional global positioning system (GPS) information helps visual recognition for geotagged photos by providing location context. However, the current GPS data only identifies the camera location, leaving the viewing direction uncertain. To produce more precise location information, i.e. the viewing direction for geotagged photos, we utilize both Google Street View and Google Earth satellite images. Our proposed system is two-pronged: 1) visual matching between a user photo and any available street views in the vicinity determine the viewing direction, and 2) when only an overhead satellite view is available, near-orthogonal view matching between the user photo and satellite imagery computes the viewing direction. Experimental results have shown the promise of the proposed framework.

We present a novel and effective algorithm for affinely skewed rotation symmetry group detection from real-world images. We define a complete skewed rotation symmetry detection problem as discovering five independent properties of a skewed rotation symmetry group: 1) the center of rotation, 2) the affine deformation, 3) the type of the symmetry group, 4) the cardinality of the symmetry group, and 5) the supporting region of the symmetry group in the image. We propose a frieze-expansion (FE) method that transforms rotation symmetry group detection into a simple, 1D translation symmetry detection problem. We define and construct a pair of rotational symmetry saliency maps, complemented by a local feature method. Frequency analysis, using Discrete Fourier Transform (DFT), is applied to the frieze-expansion patterns (FEPs) to uncover the types (cyclic, dihedral, and O2), the cardinalities, and the corresponding supporting regions, concentric or otherwise, of multiple rotation symmetry groups in an image. The phase information of the FEP is used to rectify affinely skewed rotation symmetry groups. Our result advances the state of the art in symmetry detection by offering a unique combination of region-based, feature-based, and frequency-based approaches. Experimental results on 170 synthetic and natural images demonstrate superior performance of our rotation symmetry detection algorithm over existing methods.

We generalize reflection symmetry detection to a curved glide reflection symmetry detection problem. We propose a unifying, local feature based approach for curved glide reflection symmetry detection from real, unsegmented images, where the classic reflection symmetry becomes one of four special cases. Our method detects and groups statistically dominant local reflection axes in a 3D parameter space. A curved glid reflection symmetry axis is estimated by a set of contiguous local straight reflection axes. Experimental results of the proposed algorithm on 40 real world images demonstrate promising performance.

We propose a novel and robust computational framework for automatic detection of deformed 2D wallpaper patterns in real-world images. The theory of 2D crystallographic groups provides a sound and natural correspondence between the underlying lattice of a deformed wallpaper pattern and a degree-4 graphical model. We start the discovery process with unsupervised clustering of interest points and voting for consistent lattice unit proposals. The proposed lattice basis vectors and pattern element contribute to the pairwise compatibility and joint compatibility (observation model) functions in a Markov Random Field (MRF). Thus, we formulate the 2D lattice detection as a spatial, multitarget tracking problem, solved within an MRF framework using a novel and efficient Mean-Shift Belief Propagation (MSBP) method. Iterative detection and growth of the deformed lattice are interleaved with regularized thin-plate spline (TPS) warping, which rectifies the current deformed lattice into a regular one to ensure stability of the MRF model in the next round of lattice recovery. We provide quantitative comparisons of our proposed method with existing algorithms on a diverse set of 261 real-world photos to demonstrate significant advances in accuracy and speed over the state of the art in automatic discovery of regularity in real images.

We present a novel and effective algorithm for rotation symmetry group detection from real-world images. We propose a frieze-expansion method that transforms rotation symmetry group detection into a simple translation symmetry detection problem. We define and construct a dense symmetry strength map from a given image, and search for potential rotational symmetry centers automatically. Frequency analysis, using discrete Fourier transform (DFT), is applied to the frieze-expansion patterns to uncover the types and the cardinality of multiple rotation symmetry groups in an image, concentric or otherwise. Furthermore, our detection algorithm can discriminate discrete versus continuous and cyclic versus dihedral symmetry groups, and identify the corresponding supporting regions in the image. Experimental results on over 80 synthetic and natural images demonstrate superior performance of our rotation detection algorithm in accuracy and in speed over the state of the art rotation detection algorithms.

We introduce a novel image segmentation algorithm that uses translational symmetry as the primary foreground/background separation cue. We investigate the process of identifying and analyzing image regions that present approximate translational symmetry for the purpose of image forground/background separation. In conjunction with texture-based inpainting, understanding the different see-through layers allows us to perform powerful image manipulations such as recovering a mesh-occluded background (as much as 53% occluded area) to achieve the effect of image and photo de-fencing. Our algorithm consists of three distinct phases- (1) automatically finding the skeleton structure of a potential frontal layer (fence) in the form of a deformed lattice, (2) separating foreground/background layers using appearance regularity, and (3) occluded foreground inpainting to reveal a complete, non-occluded image. Each of these three tasks presents its own special computational challenges that are not encountered in previous, general image de-layering or texture inpainting applications.

A mechanism for efficient mean-shift belief propagation (MSBP) is introduced. The novelty of our work is to use mean-shift to perform nonparametric mode-seeking on belief surfaces generated within the belief propagation framework. Belief propagation (BP) is a powerful solution for performing inference in graphical models. However, there is a quadratic increase in the cost of computation with respect to the size of the hidden variable space. While the recently proposed nonparametric belief propagation (NBP) has better performance in terms of speed, even for continuous hidden variable spaces, computation is still slow due to the particle filter sampling process. Our MSBP method only needs to compute a local grid of samples of the belief surface during each iteration. This approach needs a significantly smaller number of samples than NBP, reducing computation time, yet it also yields more accurate and stable solutions. The efficiency and robustness of MSBP is compared against other variants of BP on applications in multi-target tracking and 2D articulated body tracking.

Symmetry is one of the important cues for human and machine perception of the world. For over three decades, automatic symmetry detection from images/patterns has been a standing topic in computer vision. We present a timely, systematic, and quantitative performance evaluation of three state of the art discrete symmetry detection algorithms. This evaluation scheme includes a set of carefully chosen synthetic and real images presenting justified, unambiguous single or multiple dominant symmetries, and a pair of well-defined success rates for validation. We make our 176 test images with associated hand-labeled ground truth publicly available with this paper. In addition, we explore the potential contribution of symmetry detection for object recognition by testing the symmetry detection algorithm on three publicly available object recognition image sets (PASCAL VOC'07, MSRC and Caltech-256). Our results indicate that even after several decades of effort, symmetry detection in real-world images remains a challenging, unsolved problem in computer vision. Meanwhile, we illustrate its future potential in object recognition.

We present a novel method for automatically geo-tagging photographs of man-made environments via detection and matching of repeated patterns. Highly repetitive environments introduce numerous correspondence ambiguities and are problematic for traditional wide-baseline matching methods. Our method exploits the highly repetitive nature of urban environments, detecting multiple perspectively distorted periodic 2D patterns in an image and matching them to a 3D database of textured facades by reasoning about the underlying canonical forms of each pattern. Multiple 2D-to-3D pattern correspondences enable robust recovery of camera orientation and location. We demonstrate the success of this method in a large urban environment.

Near-regular texture (NRT), denoting deviations from otherwise symmetric wallpaper patterns, is commonly observable in the real world. Existing lattice detection algorithms capture the underlying lattice of an NRT pattern and all of its individual texels, facilitating an automated analysis of NRT. Many real world images, as in those of zebrafish larval histology arrays, depart significantly from regularity and challenge the current state of the art wallpaper group theory-based lattice detection methods. We propose an alternative 2D lattice detection algorithm that exploits translation and reflection symmetries and specific imaging cues. By outperforming existing methods on histology array images, our algorithm leads us towards complete automation of high-throughput histological image processing while broadening the spectrum of NRT computation.

Gait is an attractive biometric for vision-based human identification. Previous work on existing public data sets has shown that shape cues yield improved recognition rates compared to pure motion cues. However, shape cues are fragile to gross appearance variations of an individual, for example, walking while carrying a ball or a backpack. We introduce a novel, spatiotemporal shape variation-based frieze pattern (SVB frieze pattern) representation for gait, which captures motion information over time. The SVB frieze pattern represents normalized frame difference over gait cycles. Rows/columns of the vertical/horizontal SVB frieze pattern contain motion variation information augmented by key frame information with body shape. A temporal symmetry map of gait patterns is also constructed and combined with vertical/horizontal SVB frieze patterns for measuring the dissimilarity between gait sequences. Experimental results show that our algorithm improves gait recognition performance on sequences with and without gross differences in silhouette shape. We demonstrate superior performance of this computational framework over previous algorithms using shape cues alone on both CMU MoBo and UoS HumanID gait databases.

A near-regular texture (NRT) is a geometric and photometric deformation from its regular origin--a congruent wallpaper pattern formed by 2D translations of a single tile. A dynamic NRT is an NRT under motion. Although NRTs are pervasive in man-made and natural environments, effective computational algorithms for NRTs are few. This paper addresses specific computational challenges in modeling and tracking dynamic NRTs, including ambiguous correspondences, occlusions, and drastic illumination and appearance variations. We propose a lattice-based Markov-Random-Field (MRF) model for dynamic NRTs in a 3D spatiotemporal space. Our model consists of a global lattice structure that characterizes the topological constraint among multiple textons and an image observation model that handles local geometry and appearance variations. Based on the proposed MRF model, we develop a tracking algorithm that utilizes belief propagation and particle filtering to effectively handle the special challenges of the dynamic NRT tracking without any assumption on the motion types or lighting conditions. We provide quantitative evaluations of the proposed method against existing tracking algorithms and demonstrate its applications in video editing.

Near regular textures are pervasive in man-made and natural world. Their global regularity and local randomness pose new difficulties to the state of the art texture analysis and synthesis algorithms. We carry out a systematic comparison study on the performance of four texture synthesis algorithms on near-regular textures. Our results confirm that faithful near-regular texture synthesis remains a challenging problem for the state of the art general purpose texture synthesis algorithms. In addition, we provide comparison of human perception with computer evaluations on the quality of the texture synthesis results.

We present a 3-level hierarchical model for localizing human bodies in still images from arbitrary viewpoints. We first fit a simple tree-structured model defined on a small landmark set along the body contours by Dynamic Programming (DP). The output is a series of proposal maps that encode the probabilities of partial body configurations. Next, we fit a mixture of view-dependent models by Sequential Monte Carlo (SMC), which handles self-occlusion, anthropometric constraints, and large viewpoint changes. DP and SMC are designed to search in opposite directions such that the DP proposals are utilized effectively to initialize and guide the SMC inference. This hybrid strategy of combining deterministic and stochastic search ensures both the robustness and efficiency of DP, and the accuracy of SMC. Finally, we fit an expanded mixture model with increased landmark density through local optimization. The model hierarchy is trained on a large number of gait images. Extensive tests on cluttered images with varying poses including walking, dancing and various types of sports activities demonstrate the feasibility of the proposed approach.

We present a 2D model-based approach to localizing human body in images viewed from arbitrary and unknown angles. The central component is a statistical shape representation of the nonrigid and articulated body contours, where a nonlinear deformation is decomposed based on the concept of parts. Several image cues are combined to relate the body configuration to the observed image, with self occlusion explicitly treated. To accommodate large viewpoint changes, a mixture of view-dependent models is employed. Inference is done by direct sampling of the posterior mixture, using Sequential Monte Carlo (SMC) simulation enhanced with annealing and kernel move. The fitting method is independent of the number of mixture components, and does not require the preselection of a "correct" viewpoint. The models were trained on a large number of interactively labeled gait images. Preliminary tests demonstrated the feasibility of the proposed approach.

This paper presents an online feature selection mechanism for evaluating multiple features while tracking and adjusting the set of features used to improve tracking performance. Our hypothesis is that the features that best discriminate between object and background are also best for tracking the object. Given a set of seed features, we compute log likelihood ratios of class conditional sample densities from object and background to form a new set of candidate features tailored to the local object/background discrimination task. The two-class variance ratio is used to rank these new features according to how well they separate sample distributions of object and background pixels. This feature evaluation mechanism is embedded in a mean-shift tracking system that adaptively selects the top-ranked discriminative features for tracking. Examples are presented that demonstrate how this method adapts to changing appearances of both tracked object and scene background. We note susceptibility of the variance ratio feature selection method to distraction by spatially correlated background clutter and develop an additional approach that seeks to minimize the likelihood of distraction.

We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups. In each N-dimensional Euclidean space, a finite number of symmetry groups can characterize the structures of an infinite variety of periodic patterns. In 2D space, there are seven frieze groups describing monochrome patterns that repeat along one direction and 17 wallpaper groups for patterns that repeat along two linearly independent directions to tile the plane. We develop a set of computer algorithms that "understand" a given periodic pattern by automatically finding its underlying lattice, identifying its symmetry group, and extracting its representative motifs. We also extend this computational model for near-periodic patterns using geometric AIC. Applications of such a computational model include pattern indexing, texture synthesis, image compression, and gait analysis.

A near-regular texture deviates geometrically and photometrically from a regular congruent tiling. Although near-regular textures are ubiquitous in the man-made and natural world, they present computational challenges for state of the art texture analysis and synthesis algorithms. Using regular tiling as our anchor point, and with user-assisted lattice extraction, we can explicitly model the deformation of a near-regular texture with respect to geometry, lighting and color. We treat a deformation field both as a function that acts on a texture and as a texture that is acted upon, and develop a multi-modal framework where each deformation field is subject to analysis, synthesis and manipulation. Using this formalization, we are able to construct simple parametric models to faithfully synthesize the appearance of a near-regular texture and purposefully control its regularity.

We present a method for evaluating multiple feature spaces while tracking, and for adjusting the set of features used to improve tracking performance. Our hypothesis is that the features that best discriminate between object and background are also best for tracking the object. We develop an online feature selection mechanism based on the two-class variance ratio measure, applied to log likelihood distributions computed with respect to a given feature from samples of object and background pixels. This feature selection mechanism is embedded in a tracking system that adaptively selects the top-ranked discriminative features for tracking. Examples are presented to illustrate how the method adapts to changing appearances of both tracked object and scene background.

We introduce the term skewed symmetry groups and provide a complete theoretical treatment for 2D wallpaper groups under affine transformations. For the first time, a given periodic pattern can be classified not simply by its Euclidean symmetry group but,by its highest "potential" symmetry group under affine deformation. A concise wallpaper group migration map is constructed that separates the 17 affinely deformed wallpaper groups into small, distinct orbits. The practical value of this result includes a novel indexing and retrieval scheme for regular patterns, and a maximal-symmetry-based method for estimating shape and orientation from texture under unknown views.

Texture replacement in real images has many applications, such as interior design, digital movie making and computer graphics. The goal is to replace some specified texture patterns in an image while preserving lighting effects, shadows and occlusions. To achieve convincing replacement results we have to detect texture patterns and estimate the lighting map from a given image. Near regular planar texture patterns are considered in this paper. Given a sample texture patch, a standard tile is computed. Candidate texture regions are determined by mutual information between the standard tile and each image patch. Regions with high mutual information scores are used to estimate the admissible lighting distributions, which is represented by cached statistics. Spatial lighting change constraints are represented by a Markov random field model. Maximum a posteriori estimation of the texture segmentation and lighting map is solved in a stochastic annealing fashion, namely, the Markov chain Monte Carlo method. Visually satisfactory result is achieved using this statistical sampling model.

This paper focuses on extracting the ideal midsagittal plane (iMSP) from three-dimensional (3-D) normal and pathological neuroimages. The main challenges in this work are the structural asymmetry that may exist in pathological brains, and the anisotropic, unevenly sampled image data that is common in clinical practice. We present an edge-based, cross-correlation approach that decomposes the plane fitting problem into discovery of two-dimensional symmetry axes on each slice, followed by a robust estimation of plane parameters. The algorithm's tolerance to brain asymmetries, input image offsets and image noise is quantitatively evaluated. We find that the algorithm can extract the iMSP from input 3-D images with 1) large asymmetrical lesions; 2) arbitrary initial rotation offsets; 3) low signal-to-noise ratio or high bias field. The iMSP algorithm is compared with an approach based on maximization of mutual information registration, and is found to exhibit superior performance under adverse conditions. Finally, no statistically significant difference is found between the midsagittal plane computed by the iMSP algorithm and that estimated by two trained neuroradiologists.

Humans have an innate ability to perceive symmetry, but it is not obvious how to automate this powerful insight. In this paper the mathematical theory of frieze and wallpaper groups is used to extract visually meaningful building blocks (motifs) from a repeated pattern. A novel peak detection algorithm based on "regions of dominance" is used to automatically detect the underlying translational lattice of a repeated pattern. Following automatic classification of the pattern's symmetry group, knowledge of the interplay between rotation, reflection, glide-reflection and translation in that group leads to a small set of candidate motifs that exhibit local symmetry consistent with the global symmetry of the entire pattern. Although other work has addressed detection of the translational lattice of a repeated pattern, ours is the first to seek a principled method for determining a representative motif. Experiments show that the-resulting pattern motifs conform well with human perception.

We present a principled method of obtaining a weighted similarity metric for 3D image retrieval, firmly rooted in Bayes decision theory. The basic idea is to determine a set of most discriminative features by evaluating how well they perform on the task of classifying images according to predefined semantic categories. We propose this indirect method as a rigorous way to solve the difficult feature selection problem that comes up in most content based image retrieval tasks. The method is applied to normal and pathological neuroradiological CT images, where we take advantage of the fact that normal human brains present an approximate bilateral symmetry which is often absent in pathological brains. The quantitative evaluation of the retrieval system shows promising results.

A fitting relationship in an assembly implies that the relative location of the bodies belongs to a coset of the symmetry group of the mating feature pair. When a symmetry group is continuous, there are infinitesimal displacements which preserve the relationship. Assembly of two bodies normally involves the establishment of successively more constraining relations, many of which are fitting relations. The continuous topological structure of the associated group determines possible directions of assembly at any state in the assembly process. To accommodate to errors, it is necessary to choose a stiffness matrix appropriate to a given assembly state, which allows the robot to comply with wrenches normal to the possible assembly directions. The derivation of such matrices from a computational geometric representation of the mating feature symmetry group is considered.>

The use of symmetry groups in analysis of the kinematics aspects of assembly is described. The goal is to find how to assemble a product from a characterization of its final assembly configuration. From such an assembly configuration, a contact state lattice expressed in terms of the contacting faces of mating assembly components is generated. This contact state lattice contains all the partially ordered assembly motion sets (POAMS) that describe the intermediate contact states of an assembly component and the translational motions leading from one contact state to another. POAMS form a detailed task specification for a robot task-level planner and can be used for generating compliant control strategies. The work described forms part a kinematic assembly planning system that reasons about how parts with multiple contacting features fit together and generates assembly task specifications automatically from solid models using symmetry groups.>

When planning or describing an assembly, statements about how features should (or might) relate spatially can be expressed in terms of the symmetry groups of the features. The same is true of the interpretation of sense data. The authors show how to associate symmetry groups with features of body models created by the PADL2 system of A.A.G. Requicha and Voelcker (1982), and how to perform reasoning about spatial relationships between features of bodies occurring in an assembly in this group-theoretic context. Techniques for implementing this approach in numerical algorithms are described, with a focus on its extension to include finite rotational symmetries.>

The authors describe how to use geometric boundary models of assembly components to find mating features, thereby permitting simpler task specifications to be used. To mitigate the combinatorics of searching for a feasible correspondence between features of different bodies, boundary models produced by PADL2 (the geometric modeler) are matched against a library of standard compound features. The feasibility of mating compound features is analyzed using the symmetry groups of features.>

The paper is concerned with the use of symmetry groups as descriptors for surfaces-such symmetry groups can be used to characterise the constraints imposed between two bodies by areal contact between their surfaces. A method is presented for combining constraints imposed by spatial relationships between features (infinite geometric entities) of bodies. It consists of an algorithm for computing the intersections of infinite symmetry groups from their characteristic invariants. It is demonstrated that invariants of symmetry groups for these combined features can be computed in an efficient and practical way.>