Magnetic resonance imaging (MRI) offers visual representations of the interior of a body for clinical analysis and medical intervention. The MRI process is subjected to a variety of image processing and machine learning approaches to identify, diagnose, and classify brain diseases as well as detect abnormalities. In this paper, we propose an improved classification method for distinguishing cancerous and noncancerous tumors from brain MRI images by using Log Polar Transformation (LPT) and convolutional neural networks (CNN). The LPT has been applied for feature extraction of rotation and scaling of distorted images, while the integration of CNN introduces a machine learning approach for the tumor classification of distorted images. The dataset was formed with images of seven different brain diseases, and the training set was formed by applying CNN with the extracted features. The proposed method is then evaluated in comparison to state-of-the-art algorithms, showing a definite improvement of the former. The obtained results show that the machine learning approach offers better classification with a success rate of about 96% in both plain brain MR images and rotation- and scale-invariant brain MR images. This work also successfully classified T-1 and T-2 weighted images of neoplastic and degenerative brain diseases. The obtained accuracy is perfected by several kernel procedures, while the combined performance of the two wavelet transformations and a strong dataset make our method robust and efficient. Since no earlier study on machine learning approaches with rotated and scaled brain MRI has come to our attention, it is expected that our proposed method introduces a new paradigm in this research field.