We propose an automatic segmentation method for lumen and media with irregular contours in IntraVascular ultra-sound (IVUS) images. In contrast to most approaches that broadly label each pixel as either lumen, media, or background, we propose to approximate the lumen and media contours by closed polygonal chains. The chain vertices are placed at fixed angles obtained by dividing the entire 360\degree~angular space into equally spaced angles, and we predict their radius using an adaptive-subband-decomposition CNN. We consider two loss functions during training. The first is a novel loss function using the Jaccard Measure (JM) to quantify the similarities between the predicted lumen and media segments and the corresponding ground-truth image segments. The second loss function is the traditional Mean Squared Error. The proposed architecture significantly reduces computational costs by replacing the popular auto-encoder structure with a simple CNN as the encoder and the decoder is reduced to simply joining the consecutive predicted points. We evaluated our network on the publicly available IVUS-Challenge-2011 dataset using two performance metrics, namely JM and Hausdorff Distance (HD). The evaluation results show that our proposed network mostly outperforms the state-of-the-art lumen and media segmentation methods.