GEOMETRICAL CORRELATION AND MATCHING OF 2D IMAGE SHAPES
Keywords: Image Matching, Image Comparison, Geometric Correlation, Mathematics
Abstract. The problem of image correspondence measure selection for image comparison and matching is addressed. Many practical applications require image matching "just by shape" with no dependence on the concrete intensity or color values. Most popular technique for image shape comparison utilizes the mutual information measure based on probabilistic reasoning and information theory background. Another approach was proposed by Pytiev (so called "Pytiev morphology") based on geometrical and algebraic reasoning. In this framework images are considered as piecewise-constant 2D functions, tessellation of image frame by the set of non-intersected connected regions determines the "shape" of image and the projection of image onto the shape of other image is determined. Morphological image comparison is performed using the normalized morphological correlation coefficients. These coefficients estimate the closeness of one image to the shape of other image. Such image analysis technique can be characterized as an “"ntensity-to-geometry" matching. This paper generalizes the Pytiev morphological approach for obtaining the pure "geometry-to-geometry" matching techniques. The generalized intensity-geometrical correlation coefficient is proposed including the linear correlation coefficient and the square of Pytiev correlation coefficient as its partial cases. The morphological shape correlation coefficient is proposed based on the statistical averaging of images with the same shape. Centered morphological correlation coefficient is obtained under the condition of intensity centering of averaged images. Two types of symmetric geometrical normalized correlation coefficients are proposed for comparison of shape-tessellations. The technique for correlation and matching of shapes with ordered intensities is proposed with correlation measures invariant to monotonous intensity transformations. The quality of proposed geometrical correlation measures is experimentally estimated in the task of visual (TV) and infrared (IR) image matching. First experimental results demonstrate competitive quality and better computational performance relative to state-of-art mutual information measure.