Topology-preserving Segmentation Research Articles

A learning-based framework for topology-preserving segmentation using quasiconformal mappings

We propose the Topology-Preserving Segmentation Network, a deformation-based model that can extract objects in an image while maintaining their topological properties. This network generates segmentation masks that have the same topology as the template mask, even when trained with limited data. The network consists of two components: the Deformation Estimation Network, which produces a deformation map that warps the template mask to enclose the region of interest, and the Beltrami Adjustment Module, which ensures the bijectivity of the deformation map by truncating the associated Beltrami coefficient based on Quasiconformal theories. The proposed network can also be trained in an unsupervised manner, eliminating the need for labeled training data. This is achieved by incorporating an unsupervised segmentation loss. Our experimental results on various image datasets show that TPSN achieves better segmentation accuracy than state-of-the-art models with correct topology. Furthermore, we demonstrate TPSN’s ability to handle multiple object segmentation.

EMMCNN: An ETPS-Based Multi-Scale and Multi-Feature Method Using CNN for High Spatial Resolution Image Land-Cover Classification

Land-cover information is significant for land-use planning, urban management, and environment monitoring. This paper presented a novel extended topology-preserving segmentation (ETPS)-based multi-scale and multi-feature method using the convolutional neural network (EMMCNN) for high spatial resolution (HSR) image land-cover classification. The EMMCNN first segmented the images into superpixels using the ETPS algorithm with false-color composition and enhancement and built parallel convolutional neural networks (CNNs) with dense connections for superpixel multi-scale deep feature learning. Then, the multi-resolution segmentation (MRS) object hand-delineated features were extracted and mapped to superpixels for complementary multi-segmentation and multi-type representation. Finally, a hybrid network was designed to consist of 1-dimension CNN and multi-layer perception (MLP) with channel-wise stacking and attention-based weighting for adaptive feature fusion and comprehensive classification. Experimental results on four real HSR GaoFen-2 datasets demonstrated the superiority of the proposed EMMCNN over several well-known classification methods in terms of accuracy and consistency, with overall accuracy averagely improved by 1.74% to 19.35% for testing images and 1.06% to 8.78% for validating images. It was found that the solution combining an appropriate number of larger scales and multi-type features is recommended for better performance. Efficient superpixel segmentation, networks with strong learning ability, optimized multi-scale and multi-feature solution, and adaptive attention-based feature fusion were key points for improving HSR image land-cover classification in this study.

A Non-local Topology-Preserving Segmentation-Guided Registration Model

In this paper, we address the issue of designing a theoretically well-motivated segmentation-guided registration method capable of handling large and smooth deformations. The shapes to be matched are viewed as hyperelastic materials and more precisely as Saint Venant–Kirchhoff ones and are implicitly modeled by level set functions. These are driven in order to minimize a functional containing both a nonlinear-elasticity-based regularizer prescribing the nature of the deformation, and a criterion that forces the evolving shape to match intermediate topology-preserving segmentation results. Theoretical results encompassing existence of minimizers, existence of a weak viscosity solution of the related evolution problem and asymptotic results are given. The study is then complemented by the derivation of the discrete counterparts of the asymptotic results provided in the continuous domain. Both a pure quadratic penalization method and an augmented Lagrangian technique (involving a related dual problem) are investigated with convergence results.

A short time existence/uniqueness result for a nonlocal topology-preserving segmentation model

Motivated by a prior applied work of Vese and the second author dedicated to segmentation under topological constraints, we derive a slightly modified model phrased as a functional minimization problem, and propose to study it from a theoretical viewpoint. The mathematical model leads to a second order nonlinear PDE with a singularity at Du=0 and containing a nonlocal term. A suitable setting is thus the one of the viscosity solution theory and, in this framework, we establish a short time existence/uniqueness result as well as a Lipschitz regularity result for the solution.

Self-Repelling Snakes for Topology-Preserving Segmentation Models

The implicit framework of the level-set method has several advantages when tracking propagating fronts. Indeed, the evolving contour is embedded in a higher dimensional level-set function and its evolution can be phrased in terms of a Eulerian formulation. The ability of this intrinsic method to handle topological changes (merging and breaking) makes it useful in a wide range of applications (fluid mechanics, computer vision) and particularly in image segmentation, the main subject of this paper. Nevertheless, in some applications, this topological flexibility turns out to be undesirable: for instance, when the shape to be detected has a known topology, or when the resulting shape must be homeomorphic to the initial one. The necessity of designing topology-preserving processes arises in medical imaging, for example, in the human cortex reconstruction. It is known that the human cortex has a spherical topology so throughout the reconstruction process this topological feature must be preserved. Therefore, we propose in this paper a segmentation model based on an implicit level-set formulation and on the geodesic active contours, in which a topological constraint is enforced.