Wolfgang Förstner

A Metric for Covariance Matrices

The paper presents a metric for positive definite covariance matrices. It is a natural expression involving traces and joint eigenvalues of the matrices. It is shown to be the distance coming from a canonical invariant Riemannian metric on the space Sym + (n, ℝ) of real symmetric positive definite matrices

Towards automatic building extraction from high-resolution digital elevation models

This paper deals with an approach for extracting the 3D shape of buildings from high-resolution Digital Elevation Models (DEMs), having a grid resolution between 0.5 and 5 m. The steps of the proposed procedure increasingly use explicit domain knowledge, specifically geometric constraints in the form of parametric and prismatic building models. A new MDL-based approach generating a polygonal ground plan from segment boundaries is given. The used knowledge is object-related making adaption to data of different density and resolution simple and transparent.

A Framework for Low Level Feature Extraction

The paper presents a framework for extracting low level features. Its main goal is to explicitely exploit the information content of the image as far as possible. This leads to new techniques for deriving image parameters, to either the elimination or the elucidation of ”buttons”, like thresholds, and to interpretable quality measures for the results, which may be used in subsequent steps. Feature extraction is based on local statistics of the image function. Methods are available for blind estimation of a signal dependent noise variance, for feature preserving restoration, for feature detection and classification, and for the location of general edges and points. Their favorable scale space properties are discussed.

Extracting Buildings from Aerial Images Using Hierarchical Aggregation in 2D and 3D

We propose a model-based approach to automated 3D extraction of buildings from aerial images. We focus on a reconstruction strategy that is not restricted to a small class of buildings. Therefore, we employ a generic modeling approach which relies on the well-defined combination of building part models. Building parts are classified by their roof type. Starting from low-level image features we combine data-driven and model-driven processes within a multilevel aggregation hierarchy, thereby using a tight coupling of 2D image and 3D object modeling and processing, ending up in complex 3D building estimations of shape and location. Due to the explicit representation of well-defined processing states in terms of model-based 2D and 3D descriptions at all levels of modeling and data aggregation, our approach reveals a great potential for reliable building extraction.

Models for photogrammetric building reconstruction

Abstract The paper discusses the modeling necessary for recovering man made objects—in this case buildings—in complex scenes from digital imagery. The approach addresses all levels of image analysis for deriving semantically meaningful descriptions of the scene from the image, via the geometrical/physical model of the objects and their counterparts in the image. The central link between raster image and scene are network-like organized aspects of parts of the objects. This is achieved by generically modeling the objects using parametrized volume primitives together with the application-specific constraints, which seems to be adequate for many types of buildings. The paper sketches the various interrelationships between the different models and their use for feature extraction, hypothesis generation, and verification.

Curb reconstruction using Conditional Random Fields

This paper presents a generic framework for curb detection and reconstruction in the context of driver assistance systems. Based on a 3D point cloud, we estimate the parameters of a 3D curb model, incorporating also the curb adjacent surfaces, e.g. street and sidewalk. We apply an iterative two step approach. First, the measured 3D points, e.g., obtained from dense stereo vision, are assigned to the curb adjacent surfaces using loopy belief propagation on a Conditional Random Field. Based on this result, we reconstruct the surfaces and in particular the curb. Our system is not limited to straight-line curbs, i.e. it is able to deal with curbs of different curvature and varying height. The proposed algorithm runs in real-time on our demonstrator vehicle and is evaluated in urban real-world scenarios. It yields highly accurate results even for low curbs up to 20m distance.

Recovering Line-Networks in Images by Junction-Point Processes

The automatic extraction of line-networks from images is a well-known computer vision issue. Appearance and shape considerations have been deeply explored in the literature to improve accuracy in presence of occlusions, shadows, and a wide variety of irrelevant objects. However most existing works have ignored the structural aspect of the problem. We present an original method which provides structurally-coherent solutions. Contrary to the pixel-based and object-based methods, our result is a graph in which each node represents either a connection or an ending in the line-network. Based on stochastic geometry, we develop a new family of point processes consisting in sampling junction-points in the input image by using a Monte Carlo mechanism. The quality of a configuration is measured by a probability density which takes into account both image consistency and shape priors. Our experiments on a variety of problems illustrate the potential of our approach in terms of accuracy, flexibility and efficiency.

Image Preprocessing for Feature Extraction in Digital Intensity, Color and Range Images

The paper discusses preprocessing for feature extraction in digital intensity, color and range images. Starting from a noise model, we develop estimates for a signal dependent noise variance function and a method to transform the image, to achieve an image with signal independent noise. Establishing significance tests and the fusion of different channels for extracting linear features is shown to be simplified.

Coding Images with Local Features

We develop a qualitative measure for the completeness and complementarity of sets of local features in terms of covering relevant image information. The idea is to interpret feature detection and description as image coding, and relate it to classical coding schemes like JPEG. Given an image, we derive a feature density from a set of local features, and measure its distance to an entropy density computed from the power spectrum of local image patches over scale. Our measure is meant to be complementary to existing ones: After task usefulness of a set of detectors has been determined regarding robustness and sparseness of the features, the scheme can be used for comparing their completeness and assessing effects of combining multiple detectors. The approach has several advantages over a simple comparison of image coverage: It favors response on structured image parts, penalizes features in purely homogeneous areas, and accounts for features appearing at the same location on different scales. Combinations of complementary features tend to converge towards the entropy, while an increased amount of random features does not. We analyse the complementarity of popular feature detectors over different image categories and investigate the completeness of combinations. The derived entropy distribution leads to a new scale and rotation invariant window detector, which uses a fractal image model to take pixel correlations into account. The results of our empirical investigations reflect the theoretical concepts of the detectors.

Matching, reconstructing and grouping 3D lines from multiple views using uncertain projective geometry

We present a geometric method for (i) matching 2D line segments from multiple oriented images, (ii) optimally reconstructing 3D line segments and (iii) grouping 3D line segments to corners. The proposed algorithm uses two developments in combining projective geometry and statistics, which are described in this article: (i) the geometric entities points, lines and planes in 2D and 3D and their uncertainty are represented in homogeneous coordinates and new entities may be constructed including their propagated uncertainty. The construction can be performed directly or as an estimation. (ii) relations such as incidence, equality, parallelism and orthogonality between points, lines and planes can be tested statistically based on a given significance level. Using these tools, the resulting algorithm is straightforward and gives reasonable results. It is only based on geometric information and does not use any image intensities, though it can be extended to use other information. The matching of 3D lines does not need any thresholds other than a significance value for the hypotheses tests.