please I need a matlab code which creates a shape signature in the interval [0, 2pi], and performs fft on that signature. thank you

signature shapes from image matlab code

Abstract

We extend the shape signature based on the distance of the boundary points from the shape centroid, to the case of
fuzzy sets. The analysis of the transition from crisp to fuzzy shape descriptor is first given in the continuous case. This is
followed by a study of the specific issues induced by the discrete representation of the objects in a computer.
We analyze two methods for calculating the signature of a fuzzy shape, derived from two ways of defining a fuzzy
set: first, by its membership function, and second, as a stack of its a-cuts. The first approach is based on measuring the
length of a fuzzy straight line by integration of the fuzzy membership function, while in the second one we use averaging
of the shape signatures obtained for the individual a-cuts of the fuzzy set. The two methods, equivalent in the continuous
case for the studied class of fuzzy shapes, produce different results when adjusted to the discrete case. A statistical
study, aiming at characterizing the performances of each method in the discrete case, is done. Both methods are shown
to provide more precise descriptions than their corresponding crisp versions. The second method (based on averaged
Euclidean distance over the a-cuts) outperforms the others.


1. Introduction

For the purpose of pattern recognition, a quantitative shape analysis is often performed. One example of application is in the area of content based image retrieval useful in multimedia databases (Yoshitaka and Ichikawa, 1999; Zhang,2002). Shape properties should be chosen in a way so that they capture essential differences between objects, while maintaining invariance to position, size, and rotation. Numerous properties are available to represent and describe the shape of objects in binary images (Gonzalez and Woods, 2002). The traditional way of addressing a pattern recognition
problem consists in, first, performing a crisp segmentation of the image into object and background, and then describing the segmented object. However, this approach induces an irreversible loss of data.A crisp continuous disk, whose border corresponds to the superimposed white circle, is digitized at a low resolution. It gives the fuzzy object presented on the left picture. When such an image is segmented to get a crisp object (in this case, this is achieved with a threshold at intensity level 0.5), important information is removed. The crisp segmentation has a negative effect on the visual appearance of the object as well: the binary ‘‘disk’’ in the right picture has lost much of its visual roundness as compared to the fuzzy pre-segmented object.

Fuzzy segmentation methods have been developed in order to reduce the negative effects of this crisp representation (Udupa and Samarasekera, 1996). In real applications, fuzziness of the studied objects can arise from various reasons, such as limited acquisition conditions, but also as an intrinsic property of the object of study, which may have uncertain and/or imprecise borders. Shape signature for continuous objects One of the classical shape representation techniques consists in describing the studied object by a shape signature, which is a 1D-function representing a 2D-shape .Conventional Fourier descriptors can be obtained by applying the Fourier transform to the shape signature. Some examples of shape signatures are listed in (Kindratenko, 2003; Zhang, 2002). In this section, we analyse a signature of a continuous shape. Starting from the definition of a shape signature commonly used for crisp objects,
we propose possible extensions of this signature for fuzzy continuous objects.