This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.

We investigate the consequences of maximizing information transfer in a simple neural network (one input layer, one output layer), focussing on the case of non linear transfer functions. We assume that both receptive fields (synaptic efficacies) and transfer functions can be adapted to the environment. The main result is that, for bounded and invertible transfer functions, in the case of a vanishing additive output noise, and no input noise, maximization of information (Linsker'sinfomax principle) leads to a factorial code - hence to the same solution as required by the redundancy reduction principle of Barlow. We show also that this result is valid for linear, more generally unbounded, transfer functions, provided optimization is performed under an additive constraint, that is which can be written as a sum of terms, each one being specific to one output neuron. Finally we study the effect of a non zero input noise. We find that, at first order in the input noise, assumed to be small ...

The sensorimotor integration system can be viewed as an observer attempting to estimate its own state and the state of the environment by integrating multiple sources of information. We describe a computational framework capturing this notion, and some specific models of integration and adaptation that result from it. Psychophysical results from two sensorimotor systems, subserving the integration and adaptation of visuo-auditory maps, and estimation of the state of the hand during arm movements, are presented and analyzed within this framework. These results suggest that: (1) Spatial information from visual and auditory systems is integrated so as to reduce the variance in localization. (2) The effects of a remapping in the relation between visual and auditory space can be predicted from a simple learning rule. (3) The temporal propagation of errors in estimating the hand's state is captured by a linear dynamic observer, providing evidence for the existence of an intern...

The statistical properties of natural images suggest an optimal form of nonlinear decomposition, in which the image is decomposed using a set of linear filters at a variety of positions, scales and orientations, and these linear responses are then rectified and divided by a weighted sum of rectified responses of nearby filters. Such divisive normalization models have become widely used in modeling steady-state responses of neurons in primary visual cortex. In addition to providing a surprisingly good characterization of "typical" neurons, the statistically optimal version of the model is consistent with unusual changes in tuning properties of these neurons at different contrast levels. These results suggest that the nonlinear response properties of cortical neurons are not an accident of biophysical implementation, but serve an important functional role.

The problem of efficiently and accurately locating patterns of interest in massive time series data sets is an important and non-trivial problem in a wide variety of applications, including diagnosis and monitoring of complex systems, biomedical data analysis, and exploratory data analysis in scientific and business time series. In this paper a probabilistic approach is taken to this problem. Using piecewise linear segmentations as the underlying representation, local features (such as peaks, troughs, and plateaus) are defined using a prior distribution on expected deformations from a basic template. Global shape information is represented using another prior on the relative locations of the individual features. An appropriately defined probabilistic model integrates the local and global information and directly leads to an overall distance measure between sequence patterns based on prior knowledge. A search algorithm using this distance measure is shown to efficiently and accurately f...

ted in the first stage of retinal processing, the photoreceptor layer. In this work we measure the spectral distributions of light present in natural images by using a hyperspectral camera, 12--15 which provides a complete spectrum at each pixel. We derive human cone responses at each spatial location from the spectra, and from these we gather cone response statistics for analysis. This approach is related to that of Webster and Mollon, with the key difference that whereas they contrast the differences between various images, we study the ensemble statistics as averaged over images. Our results are qualitatively similar to those of Buchsbaum and Gottschalk, who sought to understand theoretically, by using model stimuli, how the visual system might decorrelate natural cone signals through an orthogonal linear transformation. They found that under certain conditions this can be achieved through a transformation to a luminancelike channel and a pair of blue-- yellow and red--gre

Underlying recognition is an organization of objects and their parts into classes and hierarchies. A representation of parts for recognition requires that they be invariant to rigid transformations, robust in the presence of occlusions, stable with changes in viewing geometry, and be arranged in a hierarchy. These constraints are captured in a general framework using notions of a part-line and a partitioning scheme. A proposed general principle of "form from function" motivates a particular partitioning scheme involving two types of parts, neck-based and limb-based, whose psychophysical relevance was demonstrated in [39]. Neckbased parts arise from narrowings in shape, or the local minima in distance between two points on the boundary, while limb-based parts arise from a pair of negative curvature minima which have "co-circular" tangents. In this paper, we present computational support for the limb-based and neck-based parts by showing that they are invariant, robust, stable and yield...

We undertake to develop a general theory of two-dimensional shape by elucidating several principles which any such theory should meet. The principles are organized around two basic intuitions: first, if a boundary were changed only slightly, then, in general, its shape would change only slightly. This leads us to propose an operational theory of shape based on incremental contour deformations. The second intuition is that not all contours are shapes, but rather only those that can enclose "physical" material. A theory of contour deformation is derived from these principles, based on abstract conservation principles and Hamilton-Jacobi theory. These principles are based on the work of Sethian [82, 86], the Osher-Sethian level set formulation [65], the classical shock theory of Lax [53, 54], as well as curve evolution theory for a curve evolving as a function of the curvature and the relation to geometric smoothing of Gage-Hamilton-Grayson [32, 37]. The result is a characterization of th...

We survey the main ideas behind recent research in model-based object recognition. The survey covers representations for models and images and the methods used to match them. Perceptual organization, the use of invariants, indexing schemes, and match verification are also reviewed. We conclude that there is still much room for improvement in the scope, robustness, and efficiency of object recognition methods. We identify what we believe are the ways improvements will be achieved. ii Contents 1. Introduction .................................................................................................................................... 1 2. Representation ................................................................................................................................ 3 2.1 What makes a good shape representation? ............................................................................ 3 2.2 The choice of coordinate system ..........................................

Active vision systems, and especially foveated vision systems, depend on efficient attentional mechanisms. We propose that machine visual attention should consist of both high level, context dependent components, and low level, context free components. As a basis for the context free component, we present an attention operator based on the intuitive notion of symmetry, which generalizes many of the existing methods for detecting regions of interest. It is a low level operator that can be applied successfully without a priori knowledge of the world. The resulting symmetry edge map can be applied in various low, intermediate and high level tasks, such as extraction of interest points, grouping and object recognition. In particular, we have implemented an algorithm which locates interest points in real time, and can be incorporated in active and purposive vision systems. The results agree with some psychophysical findings concerning symmetry as well as evidence concerning selection of fixation points...