Since the fractal dimension alone is not sufficient to characterize natural texture, we explore higher order geometry to accurately identify texture in biomedical images. The calculation of the fractal dimension set is based on the texture description: known as the Pseudo Matrix of the Fractal (PMF). In our research, the variants of the PMF are tested, a set of the fractal parameters are defined, and different discriminant functions are investigated. A new approach to texture classification is described. Using vectors derived from the PMF, the inner products of these normalized vectors obtained from the training groups and the test image form the measures for classification. This method is easily implemented and produces reliable classification results. The new algorithm significantly simplifies the calculation of the fractal dimension set, and the classification of texture in medical images becomes more sensitive and specific. Preliminary results have demonstrated an improved accuracy in classification on one group of eight types of realistic texture data and one set of MRI brain data.