122978488
Representation and matching of articulated shapes
We consider the problem of localizing the articulated and deformable shape of a walking person in a single view. We represent the non-rigid 2D body contour by a Bayesian graphical model whose nodes correspond to point positions along the contour. The deformability of the model is constrained by learned priors corresponding to two basic mechanisms: local non-rigid deformation, and rotation motion of the joints. Four types of image cues are combined to relate the model configuration to the observed image, including edge gradient map, foreground/background mask, skin color mask, and appearance consistency constraints. The constructed Bayes network is sparse and chain-like, enabling efficient spatial inference through sequential Monte Carlo sampling methods. We evaluate the performance of the model on images taken in cluttered, outdoor scenes. The utility of each image cue is also empirically explored.
9599152
A classification based similarity metric for 3D image retrieval
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.
5302961
A Group Theoretic Formalization of Surface Contact
The surface contacts between solids are always associated with a set of symmetries of the contacting surfaces. These symmetries form a group known as the symmetry group of the surface. In this article we develop a group theoretic formalization for describing surface contact between solids. In particular we define (1) primitive and compound features of a solid, (2) a topological characterization of these features, and (3) the symmetry groups of primitive and compound features. The symmetry group of a feature is a descriptor of the fea ture that is at once abstract and quantitative. We show how to use group theory concepts to describe the exact relative motion (position) of solids under surface contacts, which can be either rigid or articulated. The central result of this article is to prove the following: 1. When primitive features of a solid are mutually dis tinct, 1-congruent or 2-congruent, the symmetry group of a compound feature can be expressed in terms of the intersection of the symmetry groups of its primitive features. 2. When two solids have surface contact, their rela tive positions can be expressed as a coset of their common symmetry group, which in turn can be ex pressed in terms of the intersections of the symmetry groups of the primitive features involved in this con tact. These results show that using group theory to formalize surface contacts is a general approach for specifying spatial relationships and forms a sound basis for the automation of robotic task planning. One advantage of this formulation is its ability to express continuous motions between two surface- contacting solids in a computational manner and to avoid combinatorics arising from multiple relationships, especially from discrete symmetries in the assembly parts and their fea tures. At the end of this article, a geometric representation for symmetry groups and an efficient group intersection algorithm using characteristic invariants are described.
5262963
Texture replacement in real images
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.
1236601
Skewed symmetry groups
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.
5285595
Periodic Pattern Analysis under Affine Distortions Using Wallpaper Groups
In this paper, the mathematical theory of wallpaper groups is used to construct a computational tool for symmetry analysis of periodic patterns. Starting with a novel peak detection algorithm based on “regions of dominance”, an input periodic pattern can be automatically classified into one of the 17 wallpaper groups. The orbits of stabilizer subgroups within the group lead to a small set of candidate motifs that exhibit local symmetry consistent with the global symmetry of the entire pattern. We further consider affine distorted periodic patterns and show that each such pattern can be classified into a small set of symmetry groups that describe the patterns’ potential symmetries under affine transformation.
9588798
Maximal intersection of spherical polygons by an arc with applications to 4-axis machining
Many geometric optimization problems in CAD/CAM can be reduced to a maximal intersection problem on the sphere: given a set of N simple spherical polygons on the unit sphere and a real number constant L≤2π, find an arc of length L on the unit sphere that intersects as many spherical polygons as possible. Past results can only solve this maximization problem for two very restricted special cases: the arc must be either a great circle or a semi-great circle. In this paper, a simple and deterministic algorithm based on domain partitioning is presented for solving this maximal arc intersection problem in the general case when the number L is arbitrary. The algorithm is made possible by reducing the domain of the arcs to a continuous sub-space in and then establishing a quotient space partitioning in this sub-space based on a congruence relation. The number of the constituting congruent sub-regions in this quotient space partitioning is shown to have an upper-bound O(E3), where E is the total number of edges on the polygons. The proposed algorithm has a worst-case upper bound O(ME) on its running time, where M is an output-sensitive number and is bounded by O(E3). Examples including two realistic tests for 4-axis NC machining are presented.
10742303
Stability and sensitivity for congestion control in wireless networks with time varying link capacities
While extensive efforts have been devoted to providing optimization based, distributed congestion control schemes for efficient bandwidth utilization and fair allocation in both wireline and wireless networks, a common assumption therein is fixed link capacities. This unfortunately will limit the application scope in multi-hop wireless networks where channels are ever changing. In this paper, we explicitly model link capacities to be time varying and investigate congestion control problems in multi-hop wireless networks. In particular we propose a primal-dual congestion control algorithm which is proved to be trajectory stable in the absence of feedback delay. Different from system stability around a single equilibrium point, trajectory stability Guarantees the system is stable around a time varying reference trajectory. Moreover, we obtain sufficient conditions for the scheme to be locally stable in the presence of delay. Our key technique is to model time variations of capacities as perturbations to a constant link. Furthermore, to study the robustness of the algorithm against capacity variations, we investigate the sensitivity of the control scheme and through simulations to study the tradeoff between stability and sensitivity.
23025365
A structural approach to recognizing incomplete graphic objects
We propose a structural approach to recognizing incomplete graphic objects, which aims to recognize a graphic object before the user finishes drawing all its strokes. In our approach, we first create a spatial division tree (SDT) for the input object and then search for similar objects in the database of graphic object models based on this representation. Along with the SDT, an intersection-based relationship model is also proposed in our approach to describe the relationships among strokes. The experiment result has shown that our approach can significantly save user's input time for complex graphic objects. Moreover, it also proves that our approach can response to user's input in real-time and is independent of the user's drawing style.
10845590
Developing structural constraints for accurate registration of overlapping range images
Abstract Automatic image registration is an attractive and unresolved problem in the machine vision literature. This paper presents two novel structural constraints, namely proximity and closeness constraints, that improve both the accuracy and robustness of an existing motion consistency based algorithm (GICP) for automatic image registration. It also defines the conditions when such constraints are fired at specific points of the registration of two overlapping range images. The proximity constraint says that neighbouring points should be neighbouring before and after a rigid motion. The closeness constraint implements a local closest point search from the second image to the first image. While the GICP algorithm uses an exhaustive search for the closest points, in this paper, we employ the optimised k–d tree data structure to accelerate the closest point search. A large number of experiments based on real range images demonstrate that the combination of rigid motion constraints with these novel proximity and closeness constraints leads to a more accurate and robust evaluation of possible correspondences leading, in turn, to more accurate, robust and efficient automatic image registration results.
36759557
Geometrical analysis of two sets of 3D correspondence data patterns
Given two sets of image correspondence data, the analysis of the corresponding rigid body transformation that accurately describes the object's motion in 3D space is a fundamental problem in image understanding. While many methods have been put forward to analyse 3D transformations, such methods do not make use of the vector distance between feature points and angular information as constraints to analyse transformation parameters. Current methods and algorithms have also suffered from the problems of lack of efficiency, sensitivity to noise, and multiplicity of solutions. In this paper we present a novel geometrical analysis of rigid body transformations and a novel algorithm to calibrate transformation parameters based on image correspondence. The algorithm is validated through experimental calibration and a comparison is made with calibration implemented by the least squares method. We demonstrate that the proposed algorithm works well in the presence of noise and that its performance is in general superior to algorithms based on the least squares method.