Convexity Shape Prior for Binary Segmentation

Abstract

Convexity is a known important cue in human vision. We propose shape convexity as a new high-order regularization constraint for binary image segmentation. In the context of discrete optimization, object convexity is represented as a sum of three-clique potentials penalizing any 1- 0- 1 configuration on all straight lines. We show that these non-submodular potentials can be efficiently optimized using an iterative trust region approach. At each iteration the energy is linearly approximated and globally optimized within a small trust region around the current solution. While the quadratic number of all three-cliques is prohibitively high, we design a dynamic programming technique for evaluating and approximating these cliques in linear time. We also derive a second order approximation model that is more accurate but computationally intensive. We discuss limitations of our local optimization and propose gradual non-submodularization scheme that alleviates some limitations. Our experiments demonstrate general usefulness of the proposed convexity shape prior on synthetic and real image segmentation examples. Unlike standard second-order length regularization, our convexity prior does not have shrinking bias, and is robust to changes in scale and parameter selection.

Multiregion segmentation of bladder cancer structures in MRI with progressive dilated convolutional networks

“…In these works, length is typically employed as a regularizer in the energy function. More complex regularizers have been demonstrated to further boost the performance of segmentation techniques, for example, convexity or compactness . Employing such regularizers may improve performance in the current application given the compact shape of the bladder.…”

An Efficient Hierarchical Layered Graph Approach for Multi-Region Segmentation

“…For the multiple region segmentation, each region may present its own distinctive features, requiring different priors to guide the segmentation process, e.g. shape constraints [14]- [16], convexity prior [17], and boundary polarity [18], [19], allowing the customization of the segmentation to a given target region. Also, it is advantageous to explore the structural interaction between the different regions in the image, whenever it is possible.…”

Unbiased Shape Compactness for Segmentation

“…Several recent studies have shown that generic shape constraints such as convexity [10,17], compactness [1,6], axial symmetry [15], tubularity [13], skeleton consistency [12] and inter-region topology [2] can be very powerful in medical image segmentation. Such constraints can boost substantially the performances of state-of-the-art segmentation algorithms, including powerful supervised learning methods such as convolutional neural networks (CNN) [2].…”

“…Unfortunately, these shape constraints are typically high-order functionals, which yield challenging optimization problems. For instance, the recent convexity term in [10] involves a large number of non-submodular triple-cliques, and the compactness in [1] is a high-order ratio, both requiring computationally expensive approximations and iterative schemes to reach a local minimum.…”