Abstract. The purpose of this study is to discuss existing fractal-based algorithms and propose novel improvements of these algorithms to identify tumors in brain magnetic-response (MR) images. Considerable research has been pursued on fractal geometry in various aspects of image analysis and pattern recognition. Magnetic-resonance images typically have a degree of noise and randomness associated with the natural random nature of structure. Thus, fractal analysis is appropriate for MR image analysis. For tumor detection, we describe existing fractal-based techniques and propose three modified algorithms using fractal analysis models. For each new method, the brain MR images are divided into a number of pieces. The first method involves thresholding the pixel intensity values; hence, we call the technique piecewise-threshold-box-counting (PTBC) method. For the subsequent methods, the intensity is treated as the third dimension. We implement the improved piecewise-modified-box-counting (PMBC) and piecewise-triangular-prism-surface-area (PTPSA) methods, respectively. With the PTBC method, we find the differences in intensity histogram and fractal dimension between normal and tumor images. Using the PMBC and PTPSA methods, we may detect and locate the tumor in the brain MR images more accurately. Thus, the novel techniques proposed herein offer satisfactory tumor identification.