Fractal-Based Image Analysis In Radiological Applications

Abstract

We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory and to define its limitations in the area of medical image analysis for texture description, in particular, in radiological applications. A general analysis to select appropriate parameters (mask size, tolerance on fractal dimension estimation, etc.) has been performed on synthetically generated images of known fractal dimensions.Moreover, we analyzed some radiological images of human organs in which pathological areas can be observed.Input images were subdivided into blocks of 6x6 pixels; then, for each block, the fractal dimension was computed in order to create fractal images whose intensity was related to the D value, i.e., texture behaviour. Results revealed that the fractal images could point out the differences between normal and pathological tissues. By applying histogram -splitting segmentation to the fractal images, pathological areas were isolated.Two different techniques (i.e., the method developed by Pentland and the "blanket" method) were employed to obtain fractal dimension values, and the results were compared; in both cases, the appropriateness of the fractal description of the original images was verified.

Fractal Surfaces

“…Other medical imaging applications (Lundahl, Ohley et al 1985;Lundahl, Ohley et al 1986;Dellepiane, Serpico et al 1987;Chen, Daponte et al 1989;Kuklinksi, Chandra et al 1989;Caldwell, Stapleton et al 1990;Rigaut 1991;Fortin, Kumaresan et al 1992;Xiao, Chu et al 1992) of the fractal measurement ofbrightness patterns from radiography have been used for identification and image segmentation. It appears that fractal geometry appears with some frequency in natural situations, and consequently its use as a characterization tool has diagnostic utility.…”

“…Bale and Schmidt (1984) have discussed the use ofX-ray scattering to study porous fractals. Other medical and dental radiography applications of fractal geometry have been demonstrated as weH (Lundahl, Ohley et al 1985;Lundahl, Ohley et al 1986;Dellepiane, Serpico et al 1987;Chen, Daponte et al 1989;Kuklinksi, Chandra et al 1989;Caldwell, Stapleton et al 1990;Chuang, Valentino et al 1991;Rigaut 1991;Fortin, Kumaresan et al 1992). Xiao, Chu et al (1992) have used measurement of the fractal dimensions of brightness patterns for recognition in mammograms, and Recht (1993) is doing the same forpap smears.…”

Fractal-based multifeature texture description

“…Physical fractals have the self-similarity property over some limited range of scale. Among the several segmentation algorithms based on fractal dimension alone that have been proposed [3][4][5][6][7], their basic difference lays in the approach used to estimate the local D parameter of the textured surface. Their performance, however, is limited because, as it was reported by several researchers, the fractal dimension alone is not sufficient to characterize natural textures [8][9][10].…”