TRIC: Trust Region for Invariant Compactness and Its Application to Abdominal Aorta Segmentation

Unbiased Shape Compactness for Segmentation

“…Fig. 2: Dice metric for 38 subjects of the 3D FCNN [7] output with graph cut [5] regularization, with TRIC compactness [1], and with the proposed compactness.…”

“…1, third row ) shows how our compactness term can accommodate a more general class of shapes that differs significantly from tubular structures. Although TRIC [1] can also handle shapes different than a circle, multiple reference points, which form a skeleton, are required from the user in this case, a prohibitively time-consuming effort for 3D data. However, to keep the process fully automatic, only the centroid of the FCNN segmentation was provided.…”

“…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.…”

“…This study focuses on constraining segmentation functionals with shape compactness, a problem investigated previously in several works [1,6,14,11]. In segmentation, the most common compactness functional is the ratio of boundary length to area (or surface to volume in 3D) [14,11], which is related to the wellknown isoperimetric graph partitioning problem (also referred to as the Cheeger problem).…”