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.

The recognition of objects from imagery in a manner that is independent of scale, posi-tion, and orientation may be achieved by characterizing an object with a set of extracted invariant features. Several different recognition techniques have been demonstrated that utilize moments to generate such invariant features. These techniques are derived from general moment theory that is widely used throughout statistics and mechanics. In this paper, basic Cartesian moment theory is reviewed and its application to object recognition and image analysis is presented. The geometric properties of low-order moments are discussed along with the definition of several moment-space linear geometric transforms. Finally, significant research in moment-based object recognition is reviewed. 1.

A great deal of work has been done on the evaluation of information retrieval systems for alphanumeric data. The same thing can not be said about the newly emerging multimedia and image database systems. One of the central concerns in these systems is the automatic characterization of image content and retrieval of images based on similarity of image content. In this paper, we discuss effectiveness of several shape measures for content based similarity retrieval of images. The different shape measures we have implemented include outline based features (chain code based string features, Fourier descriptors, UNL Fourier features), region based features (invariant moments, Zemike moments, pseudo-Zemike moments), and combined features (invariant moments & Fourier descriptors, invariant moments & UNL Fourier features). Given an image, all these shape feature measures (vectors) are computed automatically, and the feature vector can either be used for the retrieval purpose or can be stored in the database for future queries. We have tested all of the above shape features for image retrieval on a database of 500 trademark images. The average retrieval efficiency values computed over a set of fifteen representative queries for all the methods is presented. The output of a sample shape similarity query using all the features is also shown.

Content based 3D shape retrieval for broad domains like the World Wide Web has recently gained considerable attention in Computer Graphics community. One of the main challenges in this context is the mapping of 3D objects into compact canonical representations referred to as descriptors, which serve as search keys during the retrieval process. The descriptors should have certain desirable properties like invariance under scaling, rotation and translation. Very importantly, they should possess descriptive power providing a basis for similarity measure between three-dimensional objects which is close to the human notion of resemblance. In this paper we advocate the usage of so-called 3D Zernike invariants as descriptors for content based 3D shape retrieval. The basis polynomials of this representation facilitate computation of invariants under the above transformations. Some theoretical results have already been summarized in the past from the aspect of pattern recognition and shape analysis. We provide practical analysis of these invariants along with algorithms and computational details. Furthermore, we give a detailed discussion on influence of the algorithm parameters like type and resolution of the conversion into a volumetric function, number of utilized coefficients, etc. As is revealed by our study, the 3D Zernike descriptors are natural extensions of spherical harmonics based descriptors, which are reported to be among the most successful representations at present. We conduct a comparison of 3D Zernike descriptors against these regarding computational aspects and shape retrieval performance.

Abstract — Moments are generic (and usually intuitive) descriptors that can be computed from several kinds of objects defined either from closed contours or from a set of points. In this paper, we present improvements in image-based visual servo using image moments. First, the analytical form of the interaction matrix related to the moments computed from a set of coplanar points is derived, and we show that it is different of the form obtained previously using coplanar closed contours. Six visual features are selected to design a decoupled control scheme when the object is parallel to the image plane. This nice property is then generalized to the case where the desired object position is not parallel to the image plane. Finally, experimental results are presented to illustrate the validity of our approach and its robustness with respect to modeling errors. Index Terms — Visual servoing, image moment, invariant. I.

In recent years there has been tremendous progress in 3D, immersive display and virtual reality (VR) technologies. Scientific visualization of data is one of many applications that has benefited from this progress. To fully exploit the potential of these applications in the new environment there is a need for "natural" interfaces that allow the manipulation of such displays without burdensome attachments. This paper describes the use of visual hand gesture analysis enhanced with speech recognition for developing a bimodal gesture/speech interface for controlling a 3-D display. The interface augments an existing application, VMD, which is a VR visual computing environment for molecular biologists. The free hand gestures are used for manipulating the 3-D graphical display together with a set of speech commands. We concentrate on the visual gesture analysis techniques used in developing this interface. The dual modality of gesture/speech is found to greatly aid the interaction capability....

Histogram comparison is a popular technique for image and video indexing. The complexity of the technique can be reduced by representing the histogram by its moments. In this paper, we propose two techniques to improve the performance of basic histogram/moment-based technique. First, we propose to use orthogonal Legendre moments for representing histograms. Since Legendre moments are orthogonal, they provide superior indexing performance compared to regular moments at a similar complexity. Secondly, we propose to compare the histograms of wavelet coefficients at different scales. The wavelet coefficients provide important directional information, and hence improve the performance of the basic histogram-based technique. The proposed scheme can be easily extended to color images and also be integrated into a wavelet-based image coder. I. INTRODUCTION Digital image/video indexing techniques are becoming increasingly important with the advent of broadband networks (ISDN, ATM) and image/v...

We address the problem of texture segmentation by using a novel affine invariant model. The introduction of affine invariance as a requirement for texture analysis goes beyond what is known of the human performance and also beyond the psychophysical theories. We propose to compute texture features using affine invariant intrinsic neighborhoods and affine invariant intrinsic orientation matrices. We discuss several possibilities for the definition of the channels and give comparative experimental results where an affine invariant Mumford-Shah type energy functional is used to compute the multichannel affine invariant segmentation. We prove that the method is able to retrieve faithfully the texture regions and to recover the shape from texture information in images where several textures are present. The numerical algorithm is multiscale.

In this paper, we present an on-line recognition method for hand-sketched symbols. The method is independent of stroke-order,-number, and-direction, as well as invariant to rotation, scaling, and translation of symbols. Zernike moment descriptors are used to represent symbols and three different classification techniques are compared: Support Vector Machines (SVM), Minimum Mean Distance (MMD), and Nearest Neighbor (NN). We have obtained 97 % accuracy rate on a dataset consisting of 7,410 sketched symbols using Zernike moment features and a SVM classifier. This method has been implemented in a software recognition package, HHreco [7]. 1.

We advocate the usage of 3D Zernike invariants as descriptors for 3D shape retrieval. The basis polynomials of this representation facilitate computation of invariants under rotation, translation and scaling. Some theoretical results have already been summarized in the past from the aspect of pattern recognition and shape analysis. We provide practical analysis of these invariants along with algorithms and computational details. Furthermore, we give a detailed discussion on influence of the algorithm parameters like the conversion into a volumetric function, number of utilized coefficients, etc. As is revealed by our study, the 3D Zernike descriptors are natural extensions of recently introduced spherical harmonics based descriptors. We conduct a comparison of 3D Zernike descriptors against these regarding computational aspects and shape retrieval performance using several quality measures and based on experiments on the Princeton Shape Benchmark. 1