A survey of shape analysis techniques

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A Survey of Shape Analysis Techniques
Sven Loncaric Department of Electronic Systems and Information Processing Faculty of Electrical Engineering and Computing, University of Zagreb Abbreviated title: A Survey of Shape Analysis Techniques Correspondence address: Sven Loncaric Department of Electronic Systems and Information Processing Faculty of Electrical Engineering and Computing, Universityof Zagreb Unska 3, 10000 Zagreb, Croatia Phone: +385-1-612-9891, Fax: +385-1-612-9652 E-mail: sven.loncaric@fer.hr

A Survey of Shape Analysis Techniques
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. Research in shape analysis has been motivated, in part, bystudies of human visual form perception systems. Several theories of visual form perception are brie y mentioned. Shape analysis methods are classi ed into several groups. Classi cation is determined according to the use of shape boundary or interior, and according to the type of result. An overview of the most representative methods is presented. Shape analysis Shape description Image analysisObject recognition

1 Introduction
The input to a typical image processing and analysis system is a gray-scale image of a scene containing the objects of interest. In order to understand the contents of the scene it is necessary to recognize the objects located in the scene. The shape of the object is a binary image representing the extent of the object. The shape can be thought of as asilhouette of the object e.g. obtained by illuminating the object by an in nitely distant light source. There are many imaging applications where image analysis can be reduced to the analysis of shapes, e.g. organs, cells, machine parts, characters. Shape analysis methods analyze the objects in a scene. In this paper, we concentrate on shape representation and description aspects of shape analysis.Shape representation methods result in a non-numeric representation of the original shape e.g. a graph so that the important characteristics of the shape are preserved. The word important in the above sentence typically has di erent meanings for di erent applications. Shape description refers to the methods that result in a numeric descriptor of the shape and is a step subsequent to shaperepresentation. A shape description method generates a shape descriptor vector also 1

called a feature vector from a given shape. The goal of description is to uniquely characterize the shape using its shape descriptor vector. The required properties of a shape description scheme are invariance to translation, scale, and rotation. This is required because these three transformations, by de nition,do not change the shape of the object. The input to shape analysis algorithms are shapes i.e. binary images. The procedures e.g. image segmentation used to obtain a shape from a given gray-scale image are not discussed in this paper. Shape matching or discrimination refers to methods for comparing shapes. It is used in model-based object recognition where a set of known model objects iscompared to an unknown object detected in the image. For this purpose a shape description scheme is used to determine the shape descriptor vector for each model shape and unknown shape in the scene. The unknown shape is matched to one of the model shapes by comparing the shape descriptor vectors using a metric. The problem of the shape analysis has been pursued by many authors thus resulting in a greatamount of research. A number of review papers 1, 2, 3 , as well as books 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 have been written on the subject of shape analysis.

1.1 Classi cations
Shape analysis methods can be classi ed according to many di erent criteria. Pavlidis 1 has proposed the following classi cations. The rst classi cation is based on the use of shape boundary points as...
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