A mammographic feature extraction scheme through textural and geometrical descriptors is examined to implement in a computer-aided diagnosis system for breast cancer diagnosis in this paper. This scheme is verified on a selected subset of suspicious regions (Region of Interest – ROIs) detected on a publicly available mammogram image database constructed by the Mammographic Image Analysis Society. The ROI detection is succeeded using the Chan-Vese active contour modelling after some pre-processing operations which are median filtering, morphological operations, and a region growing method performed for digitization noise reduction, artifact suppression and background removal, and pectoral muscle removal, respectively, applied on mammogram images. Then, a new adaptive convex hull approach is introduced for extracting geometrical descriptors of the ROIs accompanied by the Haralick features extracted from the gray-level co-occurrence matrices for textural description. In addition to geometrical and textural features, a hybrid mammographic feature vector is constructed by concatenating these features. All the three feature vectors are separately utilized to diagnose the ROIs via Random Forest classifier using 5-fold cross-validation. The experimental studies show that the textural features diagnose benignity more specifically and malignancy more accurately; and they are more effective on discriminating healthy ROIs when concatenated with geometrical features. Hence, a feature combination of these three features is proposed for diagnosis. The proposed feature combination is determined to be more effective for more accurate diagnoses of benignity and malignancy.