Understanding patterns of variation from rawmeasurement data remains a central goal of shape analysis. Such an understanding reveals which elements are repeated, or how elements can be derived as structured variations from a common base element. We investigate this problem in the context of 3D acquisitions of buildings. Utilizing a set of template models, we discover geometric similarities acro...

Recently, shape analysis of human organs has achieved much attention, owing to its potential to localize structural abnormalities. For a group-wise shape analysis, it is important to accurately restore the shape of a target structure in each subject and to build the inter-subject shape correspondences. To accomplish this, we propose a shape modeling method based on the Laplacian deformation fra...

The paper that introduced shape analysis sentences presented a method for extracting a sentence in first-order logic that completely characterizes a run of cpsa. Logical deduction can then be used to determine if a security goal is satisfied. This paper presents a method for importing shape analysis sentences into a proof assistant on top of a detailed theory of strand spaces. The result is a s...

Shape analysis has played a central role in many problems in vision and perception, being an active multidisciplinary research field. In this context, this paper introduces a new shape analysis approach using the well known wavelet transform and exploring shape representation by landmarks. This work shows how to obtain a time signal from the landmarks representation, which undergoes the wavelet...

In this work, we study the spectra and eigenmodes of the Hessian of various discrete surface energies and discuss applications to shape analysis. In particular, we consider a physical model that describes the vibration modes and frequencies of a surface through the eigenfunctions and eigenvalues of the Hessian of a deformation energy, and we derive a closed form representation for the Hessian (...

Modeling and understanding complex non-manifold shapes is a key issue in shape analysis and retrieval. The topological structure of a non-manifold shape can be analyzed through its decomposition into a collection of components with a simpler topology. Here, we consider a representation for arbitrary shapes, that we call ManifoldConnected Decomposition (MC-decomposition), which is based on a uni...

Successful retrieval of images by shape feature is likely to be achieved only if we can mirror human similarity judgements. Following Biederman’s theory of recognition-by-components, we postulate that shape analysis for retrieval should characterize an image by identifying properties such as collinearity, shape similarity and proximity in component boundaries. Such properties can then be used t...

Analysis of shape variability is important for diagnostic classification and understanding of biological processes. We present a novel shape analysis approach based on a multiscale medial representation. Our method examines shape variability in separate categories, such as global variability in the coarse-scale shape description and localized variability in the fine-scale description. The metho...

Shape recognition deals with the study geometric structures. Modern surface processing methods can cope with non-rigidity by measuring the lack of isometry, deal with similarity by multiplying the Euclidean arc-length by the Gaussian curvature, and manage equi-affine transformations by resorting to the special affine arc-length definition in classical affine geometry. Here, we propose a computa...