Invariant Shape Representation Research Articles

Perception of an object's global shape is best described by a model of skeletal structure in human infants.

Categorization of everyday objects requires that humans form representations of shape that are tolerant to variations among exemplars. Yet, how such invariant shape representations develop remains poorly understood. By comparing human infants (6-12 months; N=82) to computational models of vision using comparable procedures, we shed light on the origins and mechanisms underlying object perception. Following habituation to a never-before-seen object, infants classified other novel objects across variations in their component parts. Comparisons to several computational models of vision, including models of high-level and low-level vision, revealed that infants' performance was best described by a model of shape based on the skeletal structure. Interestingly, infants outperformed a range of artificial neural network models, selected for their massive object experience and biological plausibility, under the same conditions. Altogether, these findings suggest that robust representations of shape can be formed with little language or object experience by relying on the perceptually invariant skeletal structure.

Statistical shape analysis of the corpus callosum in Schizophrenia

We present a statistical shape-analysis framework for characterizing and comparing morphological variation of the corpus callosum. The midsagittal boundary of the corpus callosum is represented by a closed curve and analyzed using an invariant shape representation. The shape space of callosal curves is endowed with a Riemannian metric. Shape distances are given by the length of shortest paths (geodesics) that are invariant to shape-confounding transformations. The statistical framework enables computation of shape averages and covariances on the shape space in an intrinsic manner (unique to the shape space). The statistical framework makes use of the tangent principal component approach to achieve dimension reduction on the space of corpus callosum shapes. The advantages of this approach are - it is fully automatic, invariant, and avoids the use of landmarks to define shapes. We applied our method to determine the effects of sex, age, schizophrenia and schizophrenia-related genetic liability on callosal shape in a large sample of patients and controls and their first-degree relatives (N=218). Results showed significant age, sex, and schizophrenia effects on both global and local callosal shape structure.

Geometric Invariant Shape Representation Based on Radon and Adaptive Stationary Wavelet Transforms

This paper proposes a novel and effective geometric invariant shape representation based on Radon and adaptive stationary wavelet transforms. The proposed representation is invariant to general geometrical transformations. Instead of analyzing shapes directly in the spatial domain, the proposed method extracts shape translation and scale invariant features in radon transform domain by statistical and spectral analysis, and also represents the rotation of the shapes by shifts of the extracted features. The adaptive stationary wavelet transform is then applied to obtain energy signatures in each wavelet channel as the final geometric invariant representation. Experiment results show that the proposed shape representation is invariant to rotation, translation, and/or scale changes for images with complex inner shapes, and outperforms the other existing methods with higher recognition rates.

Wavelet approximation-based affine invariant shape representation functions

In this paper, new wavelet-based affine invariant functions for shape representation are presented. Unlike the previous representation functions, only the approximation coefficients are used to obtain the proposed functions. One of the derived functions is computed by applying a single wavelet transform; the other function is calculated by applying two different wavelet transforms with two different wavelet families. One drawback of the previously derived detail-based invariant representation functions is that they are sensitive to noise at the finer scale levels, which limits the number of scale levels that can be used. The experimental results in this paper demonstrate that the proposed functions are more stable and less sensitive to noise than the detail-based functions.

Geometric Invariant Shape Representations Using Morphological Multiscale Analysis

In this paper, we present a new geometric invariant shape representation using morphological multiscale analysis. The geometric invariant is based on the area and perimeter evolution of the shape under the action of a morphological multiscale analysis. First, we present some theoretical results on the perimeter and area evolution across the scales of a shape. In the case of similarity transformations, the proposed geometric invariant is based on a scale-normalized evolution of the isoperimetric ratio of the shape. In the case of general affine geometric transformations the proposed geometric invariant is based on a scale-normalized evolution of the area. We present some numerical experiments to evaluate the performance of the proposed models. We present an application of this technique to the problem of shape classification on a real shape database and we study the well-posedness of the proposed models in the framework of viscosity solution theory.