Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities

Intensity inhomogeneities in images constitute a considerable challenge in image segmentation. In this paper we propose a novel biconvex variational model to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. Our method assumes that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of our biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled by our model. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images which was indeed the motivation of our work

Disparity and Optical Flow Partitioning Using Extended Potts Priors

This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notation of asymptotically level stable functions we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of minimizers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method

Strain Analysis by a Total Generalized Variation Regularized Optical Flow Model

In this paper we deal with the important problem of estimating the local strain tensor from a sequence of micro-structural images realized during deformation tests of engineering materials. Since the strain tensor is defined via the Jacobian of the displacement field, we propose to compute the displacement field by a variational model which takes care of properties of the Jacobian of the displacement field. In particular we are interested in areas of high strain. The data term of our variational model relies on the brightness invariance property of the image sequence. As prior we choose the second order total generalized variation of the displacement field. This prior splits the Jacobian of the displacement field into a smooth and a non-smooth part. The latter reflects the material cracks. An additional constraint is incorporated to handle physical properties of the non-smooth part for tensile tests. We prove that the resulting convex model has a minimizer and show how a primal-dual method can be applied to find a minimizer. The corresponding algorithm has the advantage that the strain tensor is directly computed within the iteration process. Our algorithm is further equipped with a coarse-to-fine strategy to cope with larger displacements. Numerical examples with simulated and experimental data demonstrate the very good performance of our algorithm. In comparison to state-of-the-art engineering software for strain analysis our method can resolve local phenomena much better

A Variational Model for Color Assignment

Color image enhancement is a challenging task in digital imaging with many applications. This paper contributes to image enhancement methods. We propose a new variational model for color improvement in the RGB space based on a desired target intensity image. Our model improves the visual quality of the color image while it preserves the range and takes the hue of the original, badly exposed image into account without amplifying its color artifacts. To approximate the hue of the original image we use the fact that affine transforms are hue preserving. To cope with the noise in the color channels we design a particular coupled TV regularization term. Since the target intensity of the image is unaltered our model respects important image structures. Numerical results demonstrate the very good performance of our method

A Variational Model for Color Assignment

Color image enhancement is a challenging task in digital imaging with many applications. This paper contributes to image enhancement methods. We propose a new variational model for color improvement in the RGB space based on a desired target intensity image. Our model improves the visual quality of the color image while it preserves the range and takes the hue of the original, badly exposed image into account without amplifying its color artifacts. To approximate the hue of the original image we use the fact that affine transforms are hue preserving. To cope with the noise in the color channels we design a particular coupled TV regularization term. Since the target intensity of the image is unaltered our model respects important image structures. Numerical results demonstrate the very good performance of our method