Example-Based Object Detection in the Attached Image

Abstract

The paper solves the problem of detecting exemplified objects in a color image. A solution provides the representation of similar objects in the same colors, and different objects in different colors. This is achieved by combining images of object examples and a target image into a single joint image, which is represented in sequential number 1, 2, ..., etc. colors. The mentioned effect is demonstrated by detecting irises and pupils in a test image. It is explained by the fact that: a) the joint image is approximated by a hierarchy of approximations in sequential color numbers; b) the hierarchy of approximations is described by a convex sequence of approximation errors (values of the total squared error ); c) due to the convexity, the approximation errors are reduced for all approximations of the joint image. In the last explanation item, it is applied the operation of combining hierarchically organized objects into a single object, which is introduced in this paper. To produce the required hierarchy of image approximations Ward's pixel clustering is used. Ward's method is generalized for image processing by parts (within pixel subsets) that provides generation of multiple proper approximation hierarchies and accelerates the calculations. To do so, the so- called split-and-merge pixel cluster CI-method is embedded into Ward's generalized method to provide a real-life minimization of the error for image approximation in a fixed number of colors.