Convex Multi-Class Image Labeling by Simplex-Constrained Total Variation

Multi-class labeling is one of the core problems in image analysis. We show how this combinatorial problem can be approximately solved using tools from convex optimization. We suggest a novel functional based on a multidimensional total variation formulation, allowing for a broad range of data terms. Optimization is carried out in the operator splitting framework using Douglas-Rachford Splitting. In this connection, we compare two methods to solve the Rudin-Osher-Fatemi type subproblems and demonstrate the performance of our approach on single- and multichannel images

Interactive volumetric segmentation for textile micro-tomography data using wavelets and nonlocal means

This work addresses segmentation of volumetric images of woven carbon fiber textiles from micro-tomography data. We propose a semi-supervised algorithm to classify carbon fibers that requires sparse input as opposed to completely labeled images. The main contributions are: (a) design of effective discriminative classifiers, for three-dimensional textile samples, trained on wavelet features for segmentation; (b) coupling of previous step with nonlocal means as simple, efficient alternative to the Potts model; and (c) demonstration of reuse of classifier to diverse samples containing similar content. We evaluate our work by curating test sets of voxels in the absence of a complete ground truth mask. The algorithm obtains an average 0.95 F1 score on test sets and average F1 score of 0.93 on new samples. We conclude with discussion of failure cases and propose future directions toward analysis of spatiotemporal high-resolution micro-tomography images

Diffuse interface methods for multiclass segmentation of high-dimensional data

We present two graph-based algorithms for multiclass segmentation of high-dimensional data, motivated by the binary diffuse interface model. One algorithm generalizes Ginzburg-Landau (GL) functional minimization on graphs to the Gibbs simplex. The other algorithm uses a reduction of GL minimization, based on the Merriman-Bence-Osher scheme for motion by mean curvature. These yield accurate and efficient algorithms for semi-supervised learning. Our algorithms outperform existing methods, including supervised learning approaches, on the benchmark datasets that we used. We refer to Garcia-Cardona (2014) for a more detailed illustration of the methods, as well as different experimental examples. © 2014 Elsevier Ltd. All rights reserved

Multiclass Data Segmentation using Diffuse Interface Methods on Graphs

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the functional's double-well potential modified to handle the multiclass case. The first algorithm minimizes the functional using a convex splitting numerical scheme. The second algorithm is a uses a graph adaptation of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates between diffusion and thresholding. We demonstrate the performance of both algorithms experimentally on synthetic data, grayscale and color images, and several benchmark data sets such as MNIST, COIL and WebKB. We also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph Laplacian, and take advantage of the sparsity of the matrix. Experiments indicate that the results are competitive with or better than the current state-of-the-art multiclass segmentation algorithms.Comment: 14 page

Joint Image Reconstruction and Segmentation Using the Potts Model

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data

GPU-accelerated Convex Multi-phase Image Segmentation

Image segmentation is a key area of research in computer vision. Recent advances facilitated reformulation of the non-convex multi-phase segmentation problem as a convex optimization problem (see for example [2, 4, 9, 10, 13, 16]). Recently, [3] proposed a new convex relaxation approach for a class of vector-valued minimization problems, and this approach is directly applicable to the widely used classical Mumford-Shah segmentation model [11]. While the approach in [3] provides the much deserved convexification, it achieves this at the expense of an increased computational complexity due to the increased dimensionality of the reformulated problem; however, the algorithm proposed in [3] can indeed profit from a parallelized implementation. In this paper, we present a GPU-based implementation of the convex formulation for Mumford-Shah piecewise constant multi-phase image segmentation algorithm proposed in [3]. The main goal of this paper is to provide insights into the way the algorithm has been parallelized in order to obtain good speedup. We present multi-phase segmentation results both on synthetic and real images. The speedup of GPU based implementation is evaluated on three different GPUs. For sufficiently large images, the speedup achieved on GTX 285 GPU is around 40, compared to an optimized CPU implementation. The speedups obtained from GPU-based implementation are quite satisfactory. We also made our CUDA code available online

A Convex Max-Flow Segmentation of LV Using Subject-Specific Distributions on Cardiac MRI

Abstract. This work studies the convex relaxation approach to the left ventricle (LV) segmentation which gives rise to a challenging multi-region seperation with the geometrical constraint. For each region, we consider the global Bhattacharyya metric prior to evaluate a gray-scale and a ra-dial distance distribution matching. In this regard, the studied problem amounts to finding three regions that most closely match their respective input distribution model. It was previously addressed by curve evolution, which leads to sub-optimal and computationally intensive algorithms, or by graph cuts, which result in heavy metrication errors (grid bias). The proposed convex relaxation approach solves the LV segmentation through a sequence of convex sub-problems. Each sub-problem leads to a novel bound of the Bhattacharyya measure and yields the convex formulation which paves the way to build up the efficient and reliable solver. In this respect, we propose a novel flow configuration that accounts for labeling-function variations, in comparison to the existing flow-maximization con-figurations. We show it leads to a new convex max-flow formulation which is dual to the obtained convex relaxed sub-problem and does give the exact and global optimums to the original non-convex sub-problem. In addition, we present such flow perspective gives a new and simple way to encode the geometrical constraint of optimal regions. A comprehen-sive experimental evaluation on sufficient patient subjects demonstrates that our approach yields improvements in optimality and accuracy over related recent methods.

Continuous Multiclass Labeling Approaches and Algorithms

We study convex relaxations of the image labeling problem on a continuous domain with regularizers based on metric interaction potentials. The generic framework ensures existence of minimizers and covers a wide range of relaxations of the originally combinatorial problem. We focus on two specific relaxations that differ in flexibility and simplicity -- one can be used to tightly relax any metric interaction potential, while the other one only covers Euclidean metrics but requires less computational effort. For solving the nonsmooth discretized problem, we propose a globally convergent Douglas-Rachford scheme, and show that a sequence of dual iterates can be recovered in order to provide a posteriori optimality bounds. In a quantitative comparison to two other first-order methods, the approach shows competitive performance on synthetical and real-world images. By combining the method with an improved binarization technique for nonstandard potentials, we were able to routinely recover discrete solutions within 1%--5% of the global optimum for the combinatorial image labeling problem