We address the problem of two-dimensional (2-D) shape representation and matching in presence of self-intersection for large image databases. This may occur when part of an object is hidden behind another part and results in a darker section in the gray level image of the object. The boundary contour of the object must include the boundary of this part which is entirely inside the outline of the object. The Curvature Scale Space (CSS) image of a shape is a multiscale organization of its inflection points as it is smoothed. The CSS-based shape representation method has been selected for MPEG-7 standardization. We study the effects of contour self-intersection on the Curvature Scale Space image. When there is no self-intersection, the CSS image contains several arch shape contours, each related to a concavity or a convexity of the shape. Self intersections create contours with minima as well as maxima in the CSS image. An efficient shape representation method has been introduced in this paper which describes a shape using the maxima as well as the minima of its CSS contours. This is a natural generalization of the conventional method which only includes the maxima of the CSS image contours. The conventional matching algorithm has also been modified to accommodate the new information about the minima. The method has been successfully used in a real world application to find, for an unknown leaf, similar classes from a database of classified leaf images representing different varieties of chrysanthemum. For many classes of leaves, self-intersection is inevitable during the scanning of the image. Therefore the original contributions of this paper is the generalization of the Curvature Scale Space representation to the class of 2-D contours with self-intersection, and its application to the classification of Chrysanthemum leaves.

This paper describes a novel approach to multi-view 3D object retrieval. To represent each view of the object, its edge contours are extracted at different levels of scale. Each edge contour, in turn, is segmented by its curvature zero crossing points in a multi-scale fashion. This procedure is carried out using the curvature scale space technique which has been selected for MPEG-7 standardisation. A number of features are then computed for each segment of each edge contour. The image is finally represented by the locations of its segments and the values of their associated features. In response to an input query, geometric hashing is first used to find the best locally matched candidates for the verification stage where the goal is to measure the distance between the input query edge contours and the corresponding model contours after applying a proper transformation. The measurement is then optimised and used as the match value. The method has been successfully tested on a collection of 3D objects consisting of 15 aircraft of different shapes.

The feasibility of representing a three-dimensional (3-D) object with a small number of standard views is studied. The object boundary of each view is considered as a two dimensional (2-D) shape and is represented by the locations of the maxima of its curvature scale space (CSS) image contours. The idea is to identify an unknown object from an image taken from a random view by using the stored descriptions of the standard views. The CSS image has been selected for MPEG-7 standardization. The maxima of CSS image have already been used to represent 2-D shapes in different applications under similarity transforms. Since the new application involves affine transforms, we first examine the effects of general affine transforms on the representation and show that the locations of the maxima of the CSS image do not move dramatically even under large affine transformations. Our system for shape-based retrieval from large image databases is then applied to multiview 3-D object representation and recognition. Our collection of 3-D objects consists of 18 aircraft of different shapes. Three silhouette contours corresponding to random views are separately used as input for each object. Results indicate that robust and efficient 3-D free-form object recognition through multiview representation can be achieved using the CSS representation.

A shape-based method for multi-view 3-D object representation and recogni-tion is introduced and explored in this paper. 3-D objects are recognised by a small number of images taken from different views. The paper addresses the issue of automatic selection of the best and the optimum number of views for each object. The object boundary of each view is considered as a 2-D shape and is represented effectively by less than ten pairs of integer values. These values include the locations of the maxima of its Curvature Scale Space (CSS) image contours. The CSS shape descriptor is expected to be selected for MPEG-7 standardisation. An unknown object is then recognised by a single image taken from an arbitrary viewpoint. The method has been tested on a collection of 3-D objects consisting of 15 aircrafts of different shapes. Each object has been modelled using an op-timised number of silhouette contours obtained from different view points. This number varies from 5 to 25 depending on the complexity of the object and the measure of expected accuracy. A comprehensive analysis of the per-formance of the system has been given in this paper as the number of views varies. Around ten silhouette contours corresponding to random views are sepa-rately used as input for each object. Results indicated that robust and efficient 3-D free-form object recognition through multi-view representation can be achieved using the CSS representation even for large database retrieval ap-plications. 1

We introduce a new method for automatic selection of optimal views in a shape-based method of multi-view 3D object representation and recognition. A 3D object is recognised by an optimum number of images taken from different views. The object boundary of each view is considered as a 2D shape and is represented by the locations of the maxima of its curvature scale space (CSS) image contours. An unknown object is then recognised by a single image taken from an arbitrary viewpoint. The method has been tested on a collection of 3D objects consisting of 15 aircraft of different shapes. Each object has been modelled using an optimised number of silhouette contours obtained from different view points. The results obtained show that robust and efficient 3D free form object recognition through multi-view representation can be achieved using the CSS representation even for large database retrieval applications.

The maxima of curvature scale space (CSS) image have already been used to represent 2-D shapes in different applications under similarity transforms. We also consider affine transforms and examine their effect on the representation. Since the CSS image employs the arc length parametrisation which is not affine invariant, we expect some deviation in the maxima of the CSS image under affine transforms. We first examine the arc length deviation and then show that the locations of the maxima of the CSS image do not change dramatically even under large affine transformations. Applying affine transforms to every object boundary of our database of 1100 images, we construct a large database of 5500 boundary contours. The CSS representation is then used to find similar shapes from this prototype database. The results provide substantial evidence of stability of the the CSS image and its contour maxima under affine transformation. Our system for shape-based retrieval from large image databases is then applied to multi-view 3-D object representation and recognition. Our collection of 3-D objects consists of 10 aircraft of different shapes. Each object is modelled using a small number of silhouette contours obtained from different view points (four contours in one experiment and nine contours in another). Three silhouette contours corresponding to random views are separately used as input for each object. Results indicate that robust and efficient 3-D free-form object recognition through multi-view representation can be achieved using the CSS representation.

The user of an image database often wishes to retrieve all images similar to the one (s)he already has. Using some features like texture, color and shape, we can associate a feature vector to every image in the database. A fast indexing method then can be used to retrieve similar images based on their associated vectors. We use the maxima of curvature zero crossing contours of Curvature Scale Space (CSS) image as a feature vector to represent the shapes of object boundary contours. The matching algorithm which compares two sets of maxima and assigns a matching value as a measure of similarity is presented in this paper. The method is robust with respect to noise, scale and orientation changes of objects. It is also capable to retrieve objects which are similar to the mirror-image of the input boundary. We introduce the aspect ratio of the CSS image as a new parameter which can be used for indexing in conjunction with other parameters like eccentricity and circularity. The method has been tested and evaluated on a prototype database of 450 images of marine animals with a vast variety of shapes with very good results. Since shape similarity is a subjective issue, in order to evaluate the methilarity retrieval based on shape on a randomly selected small database. We then compared the results of this experiment to the outputs of our system to the same queries and on the same database. The comparison indicated a promising performance of the system.