Convex Shape Prior for Deep Neural Convolution Network based Eye Fundus Images Segmentation

Convex Shapes (CS) are common priors for optic disc and cup segmentation in eye fundus images. It is important to design proper techniques to represent convex shapes. So far, it is still a problem to guarantee that the output objects from a Deep Neural Convolution Networks (DCNN) are convex shapes. In this work, we propose a technique which can be easily integrated into the commonly used DCNNs for image segmentation and guarantee that outputs are convex shapes. This method is flexible and it can handle multiple objects and allow some of the objects to be convex. Our method is based on the dual representation of the sigmoid activation function in DCNNs. In the dual space, the convex shape prior can be guaranteed by a simple quadratic constraint on a binary representation of the shapes. Moreover, our method can also integrate spatial regularization and some other shape prior using a soft thresholding dynamics (STD) method. The regularization can make the boundary curves of the segmentation objects to be simultaneously smooth and convex. We design a very stable active set projection algorithm to numerically solve our model. This algorithm can form a new plug-and-play DCNN layer called CS-STD whose outputs must be a nearly binary segmentation of convex objects. In the CS-STD block, the convexity information can be propagated to guide the DCNN in both forward and backward propagation during training and prediction process. As an application example, we apply the convexity prior layer to the retinal fundus images segmentation by taking the popular DeepLabV3+ as a backbone network. Experimental results on several public datasets show that our method is efficient and outperforms the classical DCNN segmentation methods

Convex Shape Representation with Binary Labels for Image Segmentation: Models and Fast Algorithms

We present a novel and effective binary representation for convex shapes. We show the equivalence between the shape convexity and some properties of the associated indicator function. The proposed method has two advantages. Firstly, the representation is based on a simple inequality constraint on the binary function rather than the definition of convex shapes, which allows us to obtain efficient algorithms for various applications with convexity prior. Secondly, this method is independent of the dimension of the concerned shape. In order to show the effectiveness of the proposed representation approach, we incorporate it with a probability based model for object segmentation with convexity prior. Efficient algorithms are given to solve the proposed models using Lagrange multiplier methods and linear approximations. Various experiments are given to show the superiority of the proposed methods

Color image segmentation based on a convex K-means approach

Image segmentation is a fundamental and challenging task in image processing and computer vision. The color image segmentation is attracting more attention due to the color image provides more information than the gray image. In this paper, we propose a variational model based on a convex K-means approach to segment color images. The proposed variational method uses a combination of $l_1$ and $l_2$ regularizers to maintain edge information of objects in images while overcoming the staircase effect. Meanwhile, our one-stage strategy is an improved version based on the smoothing and thresholding strategy, which contributes to improving the accuracy of segmentation. The proposed method performs the following steps. First, we specify the color set which can be determined by human or the K-means method. Second, we use a variational model to obtain the most appropriate color for each pixel from the color set via convex relaxation and lifting. The Chambolle-Pock algorithm and simplex projection are applied to solve the variational model effectively. Experimental results and comparison analysis demonstrate the effectiveness and robustness of our method

A level set representation method for N-dimensional convex shape and applications

In this work, we present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. Convexity prior is very useful for object completion in computer vision. It is a very challenging task to design an efficient method for high dimensional convex objects representation. In this paper, we prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance function. Then, the second order condition of convex functions is used to characterize the shape convexity equivalently. We apply this new method to two applications: object segmentation with convexity prior and convex hull problem (especially with outliers). For both applications, the involved problems can be written as a general optimization problem with three constraints. Efficient algorithm based on alternating direction method of multipliers is presented for the optimization problem. Numerical experiments are conducted to verify the effectiveness and efficiency of the proposed representation method and algorithm

Geodesic Paths for Image Segmentation with Implicit Region-based Homogeneity Enhancement

Minimal paths are regarded as a powerful and efficient tool for boundary detection and image segmentation due to its global optimality and the well-established numerical solutions such as fast marching method. In this paper, we introduce a flexible interactive image segmentation model based on the Eikonal partial differential equation (PDE) framework in conjunction with region-based homogeneity enhancement. A key ingredient in the introduced model is the construction of local geodesic metrics, which are capable of integrating anisotropic and asymmetric edge features, implicit region-based homogeneity features and/or curvature regularization. The incorporation of the region-based homogeneity features into the metrics considered relies on an implicit representation of these features, which is one of the contributions of this work. Moreover, we also introduce a way to build simple closed contours as the concatenation of two disjoint open curves. Experimental results prove that the proposed model indeed outperforms state-of-the-art minimal paths-based image segmentation approaches.Comment: Published in IEEE Trans. Image Processin