Breast parenchymal density is considered a strong indicator of breast cancer risk and therefore useful for preventive tasks. Measurement of breast density is often qualitative and requires the subjective judgment of radiologists. Here we explore an automatic breast composition classification workflow based on convolutional neural networks for feature extraction in combination with a support vector machines classifier. This is compared to the assessments of seven experienced radiologists. The experiments yielded an average kappa value of 0.58 when using the mode of the radiologists' classifications as ground truth. Individual radiologist performance against this ground truth yielded kappa values between 0.56 and 0.79.