An accurate, fully automatic detection and segmentation technique for brain tumors in magnetic resonance images (MRI) is introduced. The approach basically combines geometric active contours segmentation with a deep learning-based initialization. As a pre-processing step, an anisotropic filter is used to smooth the image; afterwards, the segmentation process takes place in two phases: the first one is based on the concept of transfer learning, where a pre-trained convolutional neural network coupled with a detector is fine-tuned using a training set of 388 T1-weighted contrast enhanced MRI images that contain a brain tumor (Meningioma); this trained network is able to automatically detect the location of the tumor by generating a bounding box with certain coordinates. The second phase takes place by using the coordinates of the bounding box to initialize the geometric active contour that iteratively evolves towards the tumor's boundaries. While most of the ingredients of this processing chain are more or less well known, the main contribution of this work is in integrating the various techniques in a novel and hopefully clever form, which could take the best of both geometric segmentation algorithms and neural networks, with a relatively light training phase. The performance of such a processing network is evaluated using a separate testing set of 97 MRI images containing the same type of brain tumor. The technique proves to be remarkably effective, with a precision of 97.92%, recall of 96.91%, F-measure of 97.41% and an average Dice similarity coefficient (DSC) for segmented images above 0.95.