A Joint Variational Multichannel Multiphase Segmentation Framework

Abstract

In this paper, we propose a variational image segmentation framework for multichannel multiphase image segmentation based on the Chan-Vese active contour model. The core of our method lies in finding a variable u encoding the segmentation, by minimizing a multichannel energy functional that combines the information of multiple images. We create a decomposition of the input, either by multichannel filtering, or simply by using plain natural RGB, or medical images, which already consist of several channels. Subsequently we minimize the proposed functional for each of the channels simultaneously. Our model meets the necessary assumptions such that it can be solved efficiently by optimization techniques like the Chambolle-Pock method. We prove that the proposed energy functional has global minimizers, and show its stability and convergence with respect to noisy inputs. Experimental results show that the proposed method performs well in single-and multichannel segmentation tasks, and can be employed to the segmentation of various types of images, such as natural and texture images as well as medical images.

Variational multichannel multiclass segmentation\endgraf using unsupervised lifting with CNNs

“…The workflow proposed in [6] consists of two steps, namely the input lifting, and the subsequent minimisation of the proposed energy functional. To achive the input lifting we apply K feature enhancing transforms Φ 1 , .…”

“…The regularisation parameter for the total variation (TV) is given by λ > 0. For the efficient minimisation of our energy functional in [6], we implement a non-convex version of the first-order primaldual algorithm proposed by Chambolle and Pock in [13,3]. In this recently submitted paper [6], we have shown that at least one global minimiser of (1) exists, as well as that the minimisation of the functional is stable with respect to perturbation of the image.…”

“…As already mentioned, a strength of the method [6] is the possibility to combine it with convolutional neural networks which we implement in this work. For this purpose, a CNN consisting of four convolutional blocks is trained, each of them made up of 32 channels with convolutional kernel size 3, which divides the image into the K different feature maps.…”

“…Non-smooth level set based approaches are based on intensity values and are therefore unable to handle different types of images such as texture images. We circumvent these issues by combining the energy functional proposed in [6] with a CNN-based lifting strategy. More specifically, to this end, we train CNNs to transform a single image into a multichannel representation that serves as input to a proposed multichannel extension of the Chan-Vese active contour model.…”