Jens Keuchel

Automatic land cover analysis for Tenerife by supervised classification using remotely sensed data

Abstract Automatic land cover classification from satellite images is an important topic in many remote sensing applications. In this paper, we consider three different statistical approaches to tackle this problem: two of them, namely the well-known maximum likelihood classification (ML) and the support vector machine (SVM), are noncontextual methods. The third one, iterated conditional modes (ICM), exploits spatial context by using a Markov random field. We apply these methods to Landsat 5 Thematic Mapper (TM) data from Tenerife, the largest of the Canary Islands. Due to the size and the strong relief of the island, ground truth data could be collected only sparsely by examination of test areas for previously defined land cover classes. We show that after application of an unsupervised clustering method to identify subclasses, all classification algorithms give satisfactory results (with statistical overall accuracy of about 90%) if the model parameters are selected appropriately. Although being superior to ML theoretically, both SVM and ICM have to be used carefully: ICM is able to improve ML, but when applied for too many iterations, spatially small sample areas are smoothed away, leading to statistically slightly worse classification results. SVM yields better statistical results than ML, but when investigated visually, the classification result is not completely satisfying. This is due to the fact that no a priori information on the frequency of occurrence of a class was used in this context, which helps ML to limit the unlikely classes.

Binary partitioning, perceptual grouping, and restoration with semidefinite programming

We introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints. The approach is (tuning) parameter-free and computes high-quality combinatorial solutions using interior-point methods (convex programming) and a randomized hyperplane technique. Apart from a symmetry condition, no assumptions (such as metric pairwise interactions) are made with respect to the objective criterion. As a consequence, the approach can be applied to a wide range of problems. Applications to unsupervised partitioning, figure-ground discrimination, and binary restoration are presented along with extensive ground-truth experiments. From the viewpoint of relaxation of the underlying combinatorial problem, we show the superiority of our approach to relaxations based on spectral graph theory and prove performance bounds.

Hierarchical Image Segmentation Based on Semidefinite Programming

Image segmentation based on graph representations has been a very active field of research recently. One major reason is that pairwise similarities (encoded by a graph) are also applicable in general situations where prototypical image descriptors as partitioning cues are no longer adequate. In this context, we recently proposed a novel convex programming approach for segmentation in terms of optimal graph cuts which compares favorably with alternative methods in several aspects. In this paper we present a fully elaborated version of this approach along several directions: first, an image preprocessing method is proposed to reduce the problem size by several orders of magnitude. Furthermore, we argue that the hierarchical partition tree is a natural data structure as opposed to enforcing multiway cuts directly. In this context, we address various aspects regarding the fully automatic computation of the final segmentation. Experimental results illustrate the encouraging performance of our approach for unsupervised image segmentation.

Convex Relaxations for Binary Image Partitioning and Perceptual Grouping

We consider approaches to computer vision problems which require the minimization of a global energy functional over binary variables and take into account both local similarity and spatial context. The combinatorial nature of such problems has lead to the design of various approximation algorithms in the past which often involve tuning parameters and tend to get trapped in local minima. In this context, we present a novel approach to the field of computer vision that amounts to solving a convex relaxation of the original problem without introducing any additional parameters. Numerical ground truth experiments reveal a relative error of the convex minimizer with respect to the global optimum of below 2% on the average. We apply our approach by discussing two specific problem instances related to image partitioning and perceptual grouping. Numerical experiments illustrate the quality of the approach which, in the partitioning case, compares favorably with established approaches like the ICM-algorithm.

Image Labeling and Grouping by Minimizing Linear Functionals over Cones

We consider energy minimization problems related to image labeling, partitioning, and grouping, which typically show up at mid-level stages of computer vision systems. A common feature of these problems is their intrinsic combinatorial complexity from an optimization point-of-view. Rather than trying to compute the global minimum - a goal we consider as elusive in these cases - we wish to design optimization approaches which exhibit two relevant properties: First, in each application a solution with guaranteed degree of suboptimality can be computed. Secondly, the computations are based on clearly defined algorithms which do not comprise any (hidden) tuning parameters. In this paper, we focus on the second property and introduce a novel and general optimization technique to the field of computer vision which amounts to compute a suboptimal solution by just solving a convex optimization problem. As representative examples, we consider two binary quadratic energy functionals related to image labeling and perceptual grouping. Both problems can be considered as instances of a general quadratic functional in binary variables, which is embedded into a higher-dimensional space such that suboptimal solutions can be computed as minima of linear functionals over cones in that space (semidefinite programs). Extensive numerical results reveal that, on the average, suboptimal solutions can be computed which yield a gap below 5% with respect to the global optimum in case where this is known.

Unsupervised Image Partitioning with Semidefinite Programming

We apply a novel optimization technique, semidefinite programming, to the unsupervised partitioning of images. Representing images by graphs which encode pairwise (dis)similarities of local image features, a partition of the image into coherent groups is computed by determining optimal balanced graph cuts. Unlike recent work in the literature, we do not make any assumption concerning the objective criterion like metric pairwise interactions, for example. Moreover, no tuning parameter is necessary to compute the solution. We prove that, from the optimization point of view, our approach cannot perform worse than spectral relaxation approaches which, conversely, may completely fail for the unsupervised choice of the eigenvector threshold.