The problem of tracking curves in dense visual clutter is challenging. Kalman filtering is inadequate because it is based on Gaussian densities which, being unimodal, cannot represent simultaneous alternative hypotheses. The Condensation algorithm uses "factored sampling", previously applied to the interpretation of static images, in which the probability distribution of possible interpretations is represented by a randomly generated set. Condensation uses learned dynamical models, together with visual observations, to propagate the random set over time. The result is highly robust tracking of agile motion. Notwithstanding the use of stochastic methods, the algorithm runs in near real-time. Contents 1 Tracking curves in clutter 2 2 Discrete-time propagation of state density 3 3 Factored sampling 6 4 The Condensation algorithm 8 5 Stochastic dynamical models for curve motion 10 6 Observation model 13 7 Applying the Condensation algorithm to video-streams 17 8 Conclusions 26 A Non-line...

We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv- ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape con- texts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; reg- ularized thin plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning trans- form. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits and the COIL dataset.

This paper describes a technique for building compact models of the shape and appearance of flexible objects (such as organs) seen in 2-D images. The models are derived from the statistics of sets of labelled images of examples of the objects.

We approach recognition in the framework of deformable shape matching, relying on a new algorithm for finding correspondences between feature points. This algorithm sets up correspondence as an integer quadratic programming problem, where the cost function has terms based on similarity of corresponding geometric blur point descriptors as well as the geometric distortion between pairs of corresponding feature points. The algorithm handles outliers, and thus enables matching of exemplars to query images in the presence of occlusion and clutter. Given the correspondences, we estimate an aligning transform, typically a regularized thin plate spline, resulting in a dense correspondence between the two shapes. Object recognition is then handled in a nearest neighbor framework where the distance between exemplar and query is the matching cost between corresponding points. We show results on two datasets. One is the Caltech 101 dataset (Fei-Fei, Fergus and Perona), an extremely challenging dataset with large intraclass variation. Our approach yields a 48 % correct classification rate, compared to Fei-Fei et al’s 16%. We also show results for localizing frontal and profile faces that are comparable to special purpose approaches tuned to faces. 1.

Introduction This work describes an approach to finding objects in images based on deformable shape models. Boundary finding in two and three dimensional images is enhanced both by considering the bounding contour or surface as a whole and by using model-based shape information. Boundary finding using only local information has often been frustrated by poor-contrast boundary regions due to occluding and occluded objects, adverse viewing conditions and noise. Imperfect image data can be augmented with the extrinsic information that a geometric shape model provides. In order to exploit model-based information to the fullest extent, it should be incorporated explicitly, specifically, and early in the analysis. In addition, the bounding curve or surface can be profitably considered as a whole, rather than as curve or surface segments, because it tends to result in a more consistent solution overall. These models are best suited for objects whose diversity and irregularity of shape make

We describe an object detection system based on mixtures of multiscale deformable part models. Our system is able to represent highly variable object classes and achieves state-of-the-art results in the PASCAL object detection challenges. While deformable part models have become quite popular, their value had not been demonstrated on difficult benchmarks such as the PASCAL datasets. Our system relies on new methods for discriminative training with partially labeled data. We combine a margin-sensitive approach for data-mining hard negative examples with a formalism we call latent SVM. A latent SVM is a reformulation of MI-SVM in terms of latent variables. A latent SVM is semi-convex and the training problem becomes convex once latent information is specified for the positive examples. This leads to an iterative training algorithm that alternates between fixing latent values for positive examples and optimizing the latent SVM objective function.

Mathematical techniques are presented for the transformation of digital anatomical textbooks from the ideal to the individual, allowing for the representation of the variabilities manifest in normal human anatomies. The ideal textbook is constructed on a fixed coordinate system to contain all of the information currently available about the physical properties of neuroanatomies. This information is obtained via sensor probes such as magnetic resonance, computed axial and emission tomography, along with symbolic information such as white and gray matter tracts, nuclei, etc. Human variability associated with individuals is accommodated by defining probabilistic transformations on the textbook coordinate system, the transformations forming mathematical translation groups of high dimension. The ideal is applied to the individual patient by finding the transformation which is consistent with physical properties of deformable elastic solids and which brings the coordinate system of the textb...

A novel deformable template is presented which detects and localizes shapes in grayscale images [5]. The template is formulated as a Bayesian graphical model of a two-dimensional shape contour, and it is matched to the image using a variant of the belief propagation (BP) algorithm used for inference on graphical models. The algorithm can localize a target shape contour in a cluttered image and can accommodate arbitrary global translation and rotation of the target as well as significant shape deformations, without requiring the template to be initialized in any special way (e.g.

Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles become convex, and no bars cross while preserving the bar lengths. Furthermore, our motion is piecewise-differentiable, does not decrease the distance between any pair of vertices, and preserves any symmetry present in the initial configuration. In particular, this result settles the well-studied carpenter’s rule conjecture.

This paper proposes a framework for dealing with several problems related to the analysis of shapes. Two related such problems are the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolesio [11], we consider the characteristic functions of the subsets of R² and their distance functions. The L² norm of the difference of characteristic functions, the L # and the W norms of the difference of distance functions define interesting topologies, in particular the well-known Hausdorff distance. Because of practical considerations arising from the fact that we deal with