In this paper, we propose a hybrid approach combining traditional texture analysis methods with deep learning for the automatic detection and measurement of abdominal contour from 2-D fetal ultrasound images. Following a learning-based procedure for region of interest (ROI) localization to segment the abdominal boundary, we show that convolutional neural networks (CNNs) outperform other state-of-the-art texture features and conventional classifiers, in addressing the binary classification problem of distinguishing between abdomen versus non-abdomen regions. However, we obtain significantly better segmentation results in identifying the best ROI containing fetal abdomen, when the predictions from CNN are combined with those from gradient boosting machine (GBM) using histogram of oriented gradient (HOG) features. We trained our method on a set of 70 images and tested them on another distinct set of 70 images. We obtained a mean DICE similarity coefficient of 0.90, which shows excellent overlap with the ground truth. We report that the mean computed gestational age difference between our segmentation results and the ground truth, is within two weeks for 90% (and within one week for 70%) of the testing cases.