Matthias Heiler

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.

Natural Image Statistics for Natural Image Segmentation

We integrate a model for filter response statistics of natural images into a variational framework for image segmentation. Incorporated in a sound probabilistic distance measure, the model drives level sets toward meaningful segmentations of complex textures and natural scenes. Despite its enhanced descriptive power, our approach preserves the efficiency of level set based segmentation since each region comprises two model parameters only. Analyzing thousands of natural images we select suitable filter banks, validate the statistical basis of our model, and demonstrate that it outperforms variational segmentation methods using second-order statistics.

Controlling sparseness in non-negative tensor factorization

Non-negative tensor factorization (NTF) has recently been proposed as sparse and efficient image representation (Welling and Weber, Patt. Rec. Let., 2001). Until now, sparsity of the tensor factorization has been empirically observed in many cases, but there was no systematic way to control it. In this work, we show that a sparsity measure recently proposed for non-negative matrix factorization (Hoyer, J. Mach. Learn. Res., 2004) applies to NTF and allows precise control over sparseness of the resulting factorization. We devise an algorithm based on sequential conic programming and show improved performance over classical NTF codes on artificial and on real-world data sets.

Learning non-negative sparse image codes by convex programming

Example-based learning of codes that statistically encode general image classes is of vital importance for computational vision. Recently non negative matrix factorization (NMF) was suggested to provide image code that was both sparse and localized, in contrast to established non local methods like PCA. In this paper, we adopt and generalize this approach to develop a novel learning framework that allows to efficiently compute sparsity-controlled invariant image codes by a well defined sequence of convex conic programs. Applying the corresponding parameter-free algorithm to various image classes results in semantically relevant and transformation-invariant image representations that are remarkably robust against noise and quantization

Semidefinite clustering for image segmentation with a-priori knowledge

Graph-based clustering methods are successfully applied to computer vision and machine learning problems. In this paper we demonstrate how to introduce a-priori knowledge on class membership in a systematic and principled way: starting from a convex relaxation of the graph-based clustering problem we integrate information about class membership by adding linear constraints to the resulting semidefinite program. With our method, there is no need to modify the original optimization criterion, ensuring that the algorithm will always converge to a high quality clustering or image segmentation.

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.

Reverse-Convex programming for sparse image codes

Reverse-convex programming (RCP) concerns global optimization of a specific class of non-convex optimization problems. We show that a recently proposed model for sparse non-negative matrix factorization (NMF) belongs to this class. Based on this result, we design two algorithms for sparse NMF that solve sequences of convex second-order cone programs (SOCP). We work out some well-defined modifications of NMF that leave the original model invariant from the optimization viewpoint. They considerably generalize the sparse NMF setting to account for uncertainty in sparseness, for supervised learning, and, by dropping the non-negativity constraint, for sparsity-controlled PCA.