Lennart Wietzke

Region-Based Pose Tracking

This paper introduces a technique for region-based pose tracking without the need to explicitly compute contours. We assume a surface model of a rigid object and at least one calibrated camera view. The goal is to find the pose parameters that optimally fit the model surface to the contour of the object seen in the image. In contrast to conventional contour-based techniques, which acquire the contour to be extracted explicitly from the image, our approach optimizes an energy directly defined on the pose parameters. We show experimental results for rather challenging scenes observed with a monocular and a stereo camera system.

The Signal Multi-Vector

This work covers a fundamental problem of local phase based image analysis: the isotropic generalization of the classical 1D analytic signal to two dimensions. The analytic signal enables the analysis of local phase and amplitude information of 1D signals. Local phase, amplitude and additional orientation information can be extracted by the 2D monogenic signal with the restriction to intrinsically 1D signals. In case of 2D image signals the monogenic signal enables the rotationally invariant analysis of lines and edges. In this work we present the 2D analytic signal as a novel generalization of both the analytic signal and the 2D monogenic signal. In case of 2D image signals the 2D analytic signal enables the isotropic analysis of lines, edges, corners and junctions in one unified framework. Furthermore, we show that 2D signals are defined on a 3D projective subspace of the homogeneous conformal space which delivers a descriptive geometric interpretation of signals providing new insights on the relation of geometry and 2D image signals. Finally, we will introduce a novel algebraic signal representation, which can be regarded as an alternative and fully isomorphic representation to classical matrices and tensors. We will show the solution of isotropic intrinsically 2D image analysis without the need of steering techniques.

Dense optical flow estimation from the monogenic curvature tensor

In this paper, we address the topic of estimating two-frame dense optical flow from the monogenic curvature tensor. The monogenic curvature tensor is a novel image model, from which local phases of image structures can be obtained in a multi-scale way. We adapt the combined local and global (CLG) optical flow estimation approach to our framework. In this way, the intensity constraint equation is replaced by the local phase vector information. Optical flow estimation under the illumination change is investigated in detail. Experimental results demonstrate that our approach gives accurate estimation and is robust against noise contamination. Compared with the intensity based approach, the proposed method shows much better performance in estimating flow fields under brightness variations.

The geometry of 2D image signals

This paper covers a fundamental problem of local phase based signal processing: the isotropic generalization of the classical 1D analytic signal to two dimensions. The well known analytic signal enables the analysis of local phase and amplitude information of 1D signals. Local phase, amplitude and additional orientation information can be extracted by the 2D monogenic signal with the restriction to the subclass of intrinsically one dimensional signals. In case of 2D image signals the monogenic signal enables the rotationally invariant analysis of lines and edges. In this work we present the 2D analytic signal as a novel generalization of both the analytic signal and the 2D monogenic signal. In case of 2D image signals the 2D analytic signal enables the isotropic analysis of lines, edges, corners and junctions in one unified framework. Furthermore, we show that 2D signals exist per se in a 3D projective subspace of the homogeneous conformal space which delivers a descriptive geometric interpretation of signals providing new insights on the relation of geometry and 2D signals.

The Conformal Monogenic Signal

The conformal monogenic signalis a novel rotational invariant approach for analyzing i(ntrinsic)1D and i2D local features of two-dimensional signals (e.g. images) without the use of any heuristics. It contains the monogenic signal as a special case for i1D signals and combines scale-space, phase, orientation, energy and isophote curvature in one unified algebraic framework. The conformal monogenic signalwill be theoretically illustrated and motivated in detail by the relation of the Radon and the Riesz transform. One of the main ideas is to lift up two-dimensional signals to a higher dimensional conformal space where the signal can be analyzed with more degrees of freedom. The most interesting result is that isophote curvature can be calculated in a purely algebraic framework without the need of any derivatives.

2D Image Analysis by Generalized Hilbert Transforms in Conformal Space

This work presents a novel rotational invariant quadrature filter approach - called the conformal monogenic signal - for analyzing i(ntrinsic)1D and i2D local features of any curved 2D signal such as lines, edges, corners and junctions without the use of steering. The conformal monogenic signal contains the monogenic signal as a special case for i1D signals and combines monogenic scale space, phase, direction/orientation, energy and curvature in one unified algebraic framework. The conformal monogenic signal will be theoretically illustrated and motivated in detail by the relation of the 3D Radon transform and the generalized Hilbert transform on the sphere. The main idea is to lift up 2D signals to the higher dimensional conformal space where the signal features can be analyzed with more degrees of freedom. Results of this work are the low computational time complexity, the easy implementation into existing Computer Vision applications and the numerical robustness of determining curvature without the need of any derivatives.

Differential geometry of monogenic signal representations

This paper presents the fusion of monogenic signal processing and differential geometry to enable monogenic analyzing of local intrinsic 2D features of low level image data. New rotational invariant features such as structure and geometry (angle of intersection) of two superimposed intrinsic 1D signals will be extracted without the need of any steerable filters. These features are important for all kinds of low level image matching tasks in robot vision because they are invariant against local and global illumination changes and result from one unique framework within the monogenic scale-space.

Image Analysis by Conformal Embedding

This work presents new ideas in isotropic multi-dimensional phase based signal theory. The novel approach, called the conformal monogenic signal, is a rotational invariant quadrature filter for extracting local features of any curved signal without the use of any heuristics or steering techniques. The conformal monogenic signal contains the recently introduced monogenic signal as a special case and combines Poisson scale space, local amplitude, direction, phase and curvature in one unified algebraic framework. The conformal monogenic signal will be theoretically illustrated and motivated in detail by the relation between the Radon transform and the generalized Hilbert transform. The main idea of the conformal monogenic signal is to lift up n-dimensional signals by inverse stereographic projections to a n-dimensional sphere in ℝn+1 where the local signal features can be analyzed with more degrees of freedom compared to the flat n-dimensional space of the original signal domain. As result, it delivers a novel way of computing the isophote curvature of signals without partial derivatives. The philosophy of the conformal monogenic signal is based on the idea to use the direct relation between the original signal and geometric entities such as lines, circles, hyperplanes and hyperspheres. Furthermore, the 2D conformal monogenic signal can be extended to signals of any dimension. The main advantages of the conformal monogenic signal in practical applications are its compatibility with intrinsically one dimensional and special intrinsically two dimensional signals, the rotational invariance, the low computational time complexity, the easy implementation into existing software packages and the numerical robustness of calculating exact local curvature of signals without the need of any derivatives.

Occlusion modeling by tracking multiple objects

This article introduces a technique for region-based pose tracking of multiple objects. Our algorithm uses surface models of the objects to be tracked and at least one calibrated camera view, but does not require color, texture, or other additional properties of the objects. By optimizing a joint energy defined on the pose parameters of all objects, the proposed algorithm can explicitly handle occlusions between different objects. Tracking results in simulated as well as real world scenes demonstrate the effects of occlusion and how they are handled by the proposed method.

Dealing with Self-occlusion in Region Based Motion Capture by Means of Internal Regions

Self-occlusion is a common problem in silhouette based motion capture, which often results in ambiguous pose configurations. In most works this is compensated by a priori knowledge about the motion or the scene, or by the use of multiple cameras. Here we suggest to overcome this problem by splitting the surface model of the object and tracking the silhouette of each part rather than the whole object. The splitting can be done automatically by comparing the appearance of the different parts with the Jensen-Shannon divergence. Tracking is then achieved by maximizing the appearance differences of all involved parts and the background simultaneously via gradient descent. We demonstrate the improvements with tracking results from simulated and real world scenes.