Active Contour Models for Manifold Valued Image Segmentation

Abstract

Image segmentation is the process of partitioning an image into different regions or groups based on some characteristics like color, texture, motion or shape etc. Active contours are a popular variational method for object segmentation in images, in which the user initializes a contour which evolves in order to optimize an objective function designed such that the desired object boundary is the optimal solution. Recently, imaging modalities that produce Manifold valued images have come up, for example, DT-MRI images, vector fields. The traditional active contour model does not work on such images. In this paper, we generalize the active contour model to work on Manifold valued images. As expected, our algorithm detects regions with similar Manifold values in the image. Our algorithm also produces expected results on usual gray-scale images, since these are nothing but trivial examples of Manifold valued images. As another application of our general active contour model, we perform texture segmentation on gray-scale images by first creating an appropriate Manifold valued image. We demonstrate segmentation results for manifold valued images and texture images. * sumukh bansal@daiict.ac.in † Queries and comments to be addressed to aditya.

A Graph Framework for Manifold-Valued Data

“…3. Although Jacobi's method is in general not as efficient as related methods, e.g., the Gauss-Seidel method or successive overrelaxation methods, it has the advantage that one is able to compute all log terms and all geodesic distances d M needed in (13) in a vectorial manner, which gives a higher overall computational performance when exploiting vectorization techniques.…”

“…However, for manifold-valued images and 3D data sets, the same tasks arise as in usual image processing, e.g., denoising, inpainting or segmentation. Recently several works tackled these tasks such as [18,30,75] for inpainting, or [5,13,20] for segmentation of such data. For denoising the TV approach or Rudin-Osher-Fatemi (ROF) [70] model was introduced by [58,79] and generalized to second order methods in [8,16,18,22].…”

“…Since the image consists also of masked data values (the surrounding of the brain), those pixels are ignored during computation of the patch-distance the k−nearest neighbors. For minimization we employ the semi-implicit minimization scheme using Jacobi iterations from (13). In Figure 7b)-e) the results of the anisotropic denoising approach are shown with a maximal number N = 100 of iterations unless the average relative change 1…”

“…The resulting set of surface voxels is shown in Figure 8a), where one can see the front left side of the measured brain data slightly from above. We then apply the semi-implicit minimization scheme based on Jacobi iterations (13) for the anisotropic p-graph Laplacian model (3), λ ∈ {10, 25, 50} and neighborhoods of spatial distance ε ∈ {2, 3} in the second and third row of Figure 8, respectively. For termination of our method we use the same stopping criterion as in the last experiment.…”

Manifold-Valued Image Generation with Wasserstein Generative Adversarial Nets

“…For example, one of the most popular applications is processing phase-valued images, whose data live on either the Cycle S 1 or the Sphere S 2 , in huesaturation-value (HSV) and chromaticity-brightness (CB) color spaces. Since such HSV/CB spaces are more adapted to human color perception than the RGB space, many works like (Bergmann et al 2014;Bergmann and Weinmann 2015;Bansal and Tatu 2015;Bergmann and Weinmann 2016;Bacák et al 2016;Laus et al 2017) have studied that the image processing models based on HSV/CB components can surpass the competitors developed in the RGB space. Analogously, for a better understanding of color semantics, producing HSV/CB images in an unsupervised manner would be a good alternative for the regular image generation over the RGB space.…”