This paper presents some basics for the analysis of point clouds using the geometrically intuitive mathematical framework of conformal geometric algebra. In this framework it is easy to compute with osculating circles for the description of local curvature. Also methods for the fitting of spheres as well as bounding spheres are presented. In a nutshell, this paper provides a starting point for ...

This paper proposes a novel algorithm for individual recognition by gait. The method of Procrustes shape analysis is used to produce Procrustes Mean Shape (PMS) as a compressed representation of gait sequence. PMS is adopted as the gait signature in this paper. Instead of using the Procrustes mean shape distance as a similarity measure, we introduce shape context descriptor to measure the simil...

The 2D Fourier Descriptor is an elegant and powerful technique for 2D shape analysis. This paper intends to extend such technique to 3D. Though conceptually natural, such an extension is not trivial in that two critical problems, the spherical parametrization and invariants construction, must be solved. By using a newly developed surface parametrization method–the discrete conformal mapping (DC...

We analyze the properties of the norm of the commutator of two Hermitian matrices, showing that asymptotically it behaves like a metric, and establish its relation to joint approximate diagonalization of matrices, showing that almost-commuting matrices are almost jointly diagonalizable, and vice versa. We show an application of our results in the field of 3D shape analysis.

In this paper is presented a novel image processing tool for the extraction of geometric information in otolith images. It relies on the reconstruction of individual otolith shape histories from otolith images. Based on the proposed non-parametric level-set representation of otolith shape history, applications to the extraction of growth axes and ring structures in otolith images are first cons...

An analog VLSI circuit used to model spectral shape analysis in the central auditory system is presented. Like the receptive fields of visual cortical neurons, the spectral response fields (SRFs) of neurons in the mammalian primary auditory cortex (AI) resemble localized sinusoids of various phases (i.e., symmetry) and scale (i.e., spectral bandwidth). We use a single circuit building block to ...

We present in this paper the application of mathematical morphology operators through a transformation of the Cartesian image into another geometric space, i.e. pol-log image. The conversion into polar-logarithmic coordinates as well as the derived cyclic morphology provides satisfying results in image analysis applied to round objects or spheroid-shaped 3D-object models. As an example of appli...

We present an automated veriication technique for veriica-tion of concurrent linked lists with integer variables. We show that using our technique one can automatically verify invariants that relate (unbounded) integer variables and heap variables such as head 6 = null ! numItems > 0. The presented technique extends our previous work on composite symbolic representations with shape analysis. Th...

| Morphological size distributions and densities are frequently used as descriptors of granularity or texture within an image. They have been successfully employed in a number of image processing and analysis tasks, including shape analysis, multiscale shape representation, texture classiication, and noise ltering. In most cases however it is not possible to analytically compute these quantitie...

Statistical shape models have been extensively used in several image analysis problems, providing accurate estimates of object boundaries. However, their performance degrades if the object of interest is surrounded by a cluttered background, and the features extracted from the image contain outliers. Under these assumptions, most deformable models fail since they are attracted towards the outli...