Matthias Mühlich

Unbiased Errors-In-Variables Estimation Using Generalized Eigensystem Analysis

Recent research provided several new and fast approaches for the class of parameter estimation problems that are common in computer vision. Incorporation of complex noise model (mostly in form of covariance matrices) into errors-in-variables or total least squares models led to a considerable improvement of existing algorithms.

A considerable improvement in non-iterative homography estimation using TLS and equilibration

Abstract Let u → i and v → i be the projections of the same 3D object point in two different images (written in homogeneous coordinates). If all 3D points are restricted to lie on a plane, then the equation v → i ≃ A u → i holds for all point correspondences u → i ⇔ v → i , i =1,…, N (≃ denoting projective equivalence) with a 3×3-matrix A describing a mapping between two images of plane. The problem of estimating this mapping is known as homography estimation and constitutes a common problem in two-view motion analysis. In this paper, we will derive a new fast algorithm for homography estimation that takes image error models into account in order to improve estimation quality. In comparison to the well-known Least Squares (LS) estimation, the application of the Total Least Squares (TLS) method and a prior equilibration (which essentially consists in adjusting the error metric) leads to a considerable improvement in estimation quality. Starting out from the LS method, our approach is developed in several steps and results of each step are given, demonstrating the improvement achieved at each step. At the end, the outlier sensitivity is examined with an example for images with model violations (3D points not lying on the plane).

Improving motion and orientation estimation using an equilibrated total least squares approach

This paper outlines the ubiquitous presence of generalized orientation (or subspace) estimation problems in image analysis. We show the potential sources of bias in naive approaches to directional estimation problems, discuss countermeasures against this bias, and point out the direct relation to the total least squares problem. An improved method (using TLS and equilibration) for a precise direct motion estimation of planar objects (8 parameter motion model, homography estimation) concludes this paper.

A statistical unification of image interpolation, error concealment, and source-adapted filter design

The natural characteristics of image signals and the statistics of measurement noise are decisive for designing optimal filter sets and optimal estimation methods in signal processing. Astonishingly, this principle has so far only partially found its way into the field of image sequence processing. We show how a Wiener-type MMSE optimization criterion for the resulting image signal, based on a simple covariance model of images or image sequences, provides direct and intelligible solutions for various, apparently different, problems, such as error concealment, or adaption of filters to signal and noise statistics.

A fast algorithm for statistically optimized orientation estimation

Filtering a signal with a finite impulse response (FIR) filter introduces dependencies between the errors in the filtered image due to overlapping filter masks. If the filtering only serves as a first step in a more complex estimation problem (e.g. orientation estimation), then these correlations can turn out to impair estimation quality. n nThe aim of this paper is twofold. First, we show that orientation estimation (with estimation of optical flow being an important special case for space-time volumes) is a Total Least Squares (TLS) problem: Tp

Estimating Consistent Motion from Three Views: An Alternative to Trifocal Analysis

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Optimal estimation of homogeneous vectors

0 with sought parameter vector p and given TLS data matrix T whose statistical properties can be described with a covariance tensor. In the second part, we will show how to improve TLS estimates given this statistical information.

Ein verallgemeinerter Total Least Squares-Ansatz zur Schätzung der Epipolargeometrie

The main goal of this paper is to introduce methods for three-view motion analysis that do not need threefold correspondences in the image planes as the well-known trifocal tensor methods do. With this characteristic, the proposed method is a practically very advantageous approach for (ego-)motion analysis and structure from motion. The proposed method starts with three two-view parameter estimates generated by Hartley/Muhlich-equilibrated TLS solutions, enforces geometrical consistency and iteratively optimizes the distances from the set of epipolar lines.

Robuste Bewegungsschätzung in planaren Welten aus monokularen Bildsequenzen

Estimation of inhomogeneous vectors is well-studied in estimation theory. For instance, given covariance matrices of input data allow to compute optimal estimates and characterize their certainty. But a similar statement does not hold for homogeneous vectors and unfortunately, the majority of estimation problems arising in computer vision refers to such homogeneous vectors... n nThe aim of this paper is twofold: First, we will describe several iterative estimation schemes for homogeneous estimation problems in a unified framework, thus presenting the missing link between those apparently different approaches. And secondly, we will present a novel approach called IETLS (for iterative equilibrated total least squares) which is insensitive to data preprocessing and shows better stability in presence of higher noise levels where other schemes often fail to converge.

A statistical extension of normalized convolution and its usage for image interpolation and filtering

Kern dieses Beitrags ist (in Erweiterung von [6]) die statistische Analyse des 8 + n-Punkte Algorithmus’ zur Bestimmung der Fundamentalmatrix. Dadurch gelingt es, eine Verbesserung dieses als sehr empfindlich geltenden Verfahrens zu erreichen, die uber die Wirkung der von Hartley vorgeschlagenen Normalisierungstransformationen hinausgeht. An dem hier betrachteten „klassischen“Vision-Problem wird deutlich, das die moglichst genaue statistische Analyse des Fehlerverhaltens eines Algorithmus’ keine akademische Fingerubung, sondern eine zwingende Notwendigkeit auf dem Weg zu zuverlassigen und praxistauglichen Verfahren ist.