## 4 Object Recognition  
Shape is an important visual feature; however, its description is a difficult task. Real-world objects are three dimensional, and when a 3-D object is projected onto a 2-D plane (as happens, for example, when receiving input from a camera), one dimension of the object is lost. Silhouettes extracted from a projection partially represent a 3-D object and can dramatically change depending on the projection axis. In contrast to color and texture, shapes are usually extracted after the image has been segmented into regions (for example, after separation of background and foreground); for this reason the shape's contour is typically corrupted by noise, arbitrary distortions, and occlusions. Thus, the main  
Figure 9: Basic texture analysis steps. requirement for the shape descriptors is to be robust to the deformations mentioned, and to be scale and rotation invariant. We have further investigated the robustness of the descriptor (feature extractor) used in _FPFT_ and applied it to the retrieval of silhouettes resulting from image segmentation. By using the same feature extraction technique, our method is able to capture the characteristics of the boundary contour, and recognize/retrieve shapes from a database. The feature extractor used in _FPFT_ is re-tasked here as the first phase of an effective shape recognition algorithm: _RBRC_ (Retrieval Based on Rotation-invariant Classification). Many ad-hoc shape representation techniques have been proposed and evaluated by measuring how precisely they retrieve similar shapes from a reference database. Shape representation techniques have been categorized into contour-based and region-based descriptors ([PERSON] [11]). Contour-based methods extract shape features from the object boundaries, which are crucial to human perception of shape similarity. If features are extracted by using a continuous approach the feature vector is derived from the entire shape boundary and the measure of shape similarity is either point-based matching or feature-based matching. In the case of discrete approach the shape boundary is broken into segments, called primitives, using techniques such as polygonal approximation, curvature decomposition, or curve fitting. The resulting shape descriptor is usually a string or a graph, allowing the use of a similarity measure based on string or graph matching. In contrast, region-based methods do not necessarily rely on boundaries, but instead extract shape features by looking at the shape as a whole. All pixels within a region are taken into account to obtain the shape representation. Since they extract features from internal and possibly boundary pixels, region-based methods can describe simple objects with or without holes as well as complex objects consisting of disconnected regions. Many shape descriptors have been proposed, each with its advantages and disadvantages. Since it is believed that humans discriminate shapes based primarily on their boundaries, contour-based methods have been often been favored over region-based methods. Techniques with which we have compared our algorithm include:  
_Curvature Scale Space_ (CSS) shape descriptors ([PERSON], [PERSON], and [PERSON] [12]) reduce the contours of a shape into sections of convex and concave curvature by determining the position of points at which the curvature is zero. To achieve this, the shape boundary is analyzed at different scales, _i.e._, filtering the contour using low-pass Gaussian filters of variable widths. _Visual parts_([PERSON] and [PERSON] [13]) is an algorithm based on the idea that a unique sub-assembly of an object can often provide strong cues in recognizing the larger object of which they are a distinct part. _Shape contexts_ (SC) ([PERSON], [PERSON], and [PERSON] [14]) is a correspondence-based shape matching technique where the shape's contour is sampled using a subset of points.