Intravascular optical coherence tomography (IOCT) is a modality that provides sufficient resolution for very accurate visualization of localized cardiovascular conditions, such as coronary artery calcification (CAC). CAC quantification in IOCT images is still performed mostly manually, which is time consuming, considering that each IOCT exam has more than two hundred 2D slices. An automated method for CAC detection in IOCT would add valuable information for clinicians when treating patients with coronary atherosclerosis. In this context, we propose an approach that uses a fully connected neural network (FCNN) for CAC detection in IOCT images using a small training dataset. In our approach, we transform the input image to polar coordinate transformation using as reference the centroid from the lumen segmentation, that restricts the variability in CAC spatial position, which we proved to be beneficial for the CNN training with few training data. We analyzed 51 slices from in-vivo human coronaries and the method achieved 63.6% sensitivity and 99.8% specificity for segmenting CAC. Our results demonstrate that it is possible to successfully detect and segment calcific plaques in IOCT images using FCNNs.