Extraction of Affine Invariant Features Using Fractal

An approach based on fractal is presented for extracting affine invariant features. Central projection transformation is employed to reduce the dimensionality of the original input pattern, and general contour (GC) of the pattern is derived. Affine invariant features cannot be extracted from GC directly due to shearing. To address this problem, a group of curves (which are called shift curves) are constructed from the obtained GC. Fractal dimensions of these curves can readily be computed and constitute a new feature vector for the original pattern. The derived feature vector is used in question for pattern recognition. Several experiments have been conducted to evaluate the performance of the proposed method. Experimental results show that the proposed method can be used for object classification. 1. Introduction The images of an object taken from different viewpoints often suffer from perspective distortions. For this reason, features extracted from the image of an object should be tolerant to an appropriate class of geometric transformation (such as translation, rotation, scaling, and shearing). A perspective transformation between two views can be approximated with an affine transformation if the object is planar and far away from the image plane [1]. Therefore, the extraction of affine invariant features plays a very important role in object recognition and has been found application in many fields such as shape recognition and retrieval [2, 3], watermarking [4], identification of aircrafts [5, 6], texture classification [7], image registration [8], and contour matching [9]. Many algorithms have been developed for affine invariant features extraction [10–12]. Based on whether the features are extracted from the contour only or from the whole shape region, the approaches can be classified into two main categories: region-based methods and contour-based methods. Contour-based methods provide better data reduction [13], but they are inapplicable to objects with several separable components. Region-based methods can achieve high accuracy but usually at the expense of high computational demands, for good overviews of the various techniques refer to [13–16]. Central projection transformation (CPT) [17] can be used to combine contour-based methods and region-based methods together. However, CPT cannot be used to extract affine invariant features directly. In this paper, we extract affine invariant features by integrating CPT and fractal. The essential advantage of fractal technique descriptor is that it can greatly speed up computation [17]. Fractal,