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Daniel Cremers

Publications and source records attributed to Daniel Cremers.

4 recordsLinked to original sources

Dynamical statistical shape priors for level set-based tracking.

In recent years, researchers have proposed introducing statistical shape knowledge into level set-based segmentation methods in order to cope with insufficient low-level information. While these priors were shown to drastically improve the segmentation of familiar objects, so far the focus has been on statistical shape priors which are static in time. Yet, in the context of tracking deformable objects, it is clear that certain silhouettes (such as those of a walking person) may become more or less likely over time. In this paper, we tackle the challenge of learning dynamical statistical models for implicitly represented shapes. We show how these can be integrated as dynamical shape priors in a Bayesian framework for level set-based image sequence segmentation. We assess the effect of such shape priors "with memory" on the tracking of familiar deformable objects in the presence of noise and occlusion. We show comparisons between dynamical and static shape priors, between models of pure deformation and joint models of deformation and transformation, and we quantitatively evaluate the segmentation accuracy as a function of the noise level and of the camera frame rate. Our experiments demonstrate that level set-based segmentation and tracking can be strongly improved by exploiting the temporal correlations among consecutive silhouettes which characterize deforming shapes.

Algorithms↗

Integral invariants for shape matching.

For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database.

Algorithms↗

Efficient kernel density estimation of shape and intensity priors for level set segmentation.

We propose a nonlinear statistical shape model for level set segmentation which can be efficiently implemented. Given a set of training shapes, we perform a kernel density estimation in the low dimensional subspace spanned by the training shapes. In this way, we are able to combine an accurate model of the statistical shape distribution with efficient optimization in a finite-dimensional subspace. In a Bayesian inference framework, we integrate the nonlinear shape model with a nonparametric intensity model and a set of pose parameters which are estimated in a more direct data-driven manner than in previously proposed level set methods. Quantitative results show superior performance (regarding runtime and segmentation accuracy) of the proposed nonparametric shape prior over existing approaches.

Algorithms↗

Traveling waves of excitation in neural field models: equivalence of rate descriptions and integrate-and-fire dynamics.

Field models provide an elegant mathematical framework to analyze large-scale patterns of neural activity. On the microscopic level, these models are usually based on either a firing-rate picture or integrate-and-fire dynamics. This article shows that in spite of the large conceptual differences between the two types of dynamics, both generate closely related plane-wave solutions. Furthermore, for a large group of models, estimates about the network connectivity derived from the speed of these plane waves only marginally depend on the assumed class of microscopic dynamics. We derive quantitative results about this phenomenon and discuss consequences for the interpretation of experimental data.

Animals↗