Reproducible kernel Hilbert space based global and local image segmentation

Abstract

Image segmentation is the task of partitioning an image into individual objects, and has many important applications in a wide range of fields. The majority of segmentation methods rely on image intensity gradient to define edges between objects. However, intensity gradient fails to identify edges when the contrast between two objects is low. In this paper we aim to introduce methods to make such weak edges more prominent in order to improve segmentation results of objects of low contrast. This is done for two kinds of segmentation models: global and local. We use a combination of a reproducing kernel Hilbert space and approximated Heaviside functions to decompose an image and then show how this decomposition can be applied to a segmentation model. We show some results and robustness to noise, as well as demonstrating that we can combine the reconstruction and segmentation model together, allowing us to obtain both the decomposition and segmentation simultaneously.

Evaluation of a hybrid pipeline for automated segmentation of solid lesions based on mathematical algorithms and deep learning

“…After windowing and selecting the uppermost and lowermost slice for segmentation on either a post-EVAR aneurysm or a selected organ from the BraTS or Abdomen datasets, we ran our variational model 10 . This original model uses an enhanced method of edge detection, which allows for images containing low contrast to be segmented effectively.…”

“…This original model uses an enhanced method of edge detection, which allows for images containing low contrast to be segmented effectively. Following edge detection, the region of interest is segmented based on image intensity and pixel location in the image 10 . The variational method provided us with a good but not perfect initial segmentation, as some regions may contain no contrast at the boundary.…”

“…We have developed our own fully automated hybrid approach (a hybrid segmentation pipeline) for volumetric segmentation, which combines a recently developed variational model 10 with a deep learning algorithm. In this work, we tested the accuracy of this hybrid segmentation pipeline.…”

On a Variational and Convex Model of the Blake–Zisserman Type for Segmentation of Low-Contrast and Piecewise Smooth Images

“…Successful results have been obtained. See [11][12][13], among others. However, for images that have weak edges possibly buried in noise and blur, the Mumford-Shah type models may fail to capture the 'discontinuities of second kind' or gradient discontinuity, which may be called the staircasing effect for gradients.…”

Selective Image Segmentation Models Using Three Distance Functions

“…According to Yearwood (2018), to obtain minimum or maximum optimality, variational methods use the calculus of variations to optimize the cost function. The methods introduced by Kass et al (1988), Mumford and Shah (1989), Perona and Malik (1990), Caselles et al (1997), Chan and Vese (2001), Gout et al (2005), Chan et al (2006), Rada and Chen (2011), Brown et al (2012), Getreuer (2012), Spencer and Chen (2015), Bastan et al (2017), Jumaat and Chen (2019), and Burrows et al (2020), as well as other variational methods, were proposed to improve the efficiency of segmentation results.…”