Toward a symbolic representation of intensity changes in images

The problem of symbolic representation of gray value variations is studied, especially with respect to the gradient of the image function. The goal is to relate the results of this analysis to the structure of the picture, which is determined by the physics of the image generation process. The operators for the detection of gray value transitions are the first derivatives of two-dimensional Gaussians with different widths whose positive and negative parts are separately normalized to plus 1 and minus 1, respectively. Candidates for contour points are the maximal magnitudes of the gray value gradient for different scales in the direction of the gradient. Based on the output of such a bank of gradient filters, a procedure is proposed in order to select automatically a suitable scale and with that the size of the right convolution kernel. In this way, the application of poorly adapted filters, which make the exact localization of gray value corners or T-, X-, and Y-junctions more difficul t, can be avoided. For images of real scenes, possible gaps at such junctions are discussed, and possibilities for the closure of some of these gaps are demonstrated if the extrema of the magnitude of the grav value gradient are used. Closed chains of contour points define regions whose gray values can be reconstructed approximately from the attributes of contour points. Results of the segmentation are shown for various pictures of real scenes.