Qualifying 4D Deforming Surfaces by Registered Differential Features

Abstract

Recent advances in 4D data acquisition systems in the field of Computer Vision have opened up many exciting new possibilities for the interpretation of complex moving surfaces. However, a fundamental problem is that this has also led to a huge increase in the volume of data to be handled. Attempting to make sense of this wealth of information is then a core issue to be addressed if such data can be applied to more complex tasks. Similar problems have been historically encountered in the analysis of 3D static surfaces, leading to the extraction of higher-level features based on analysis of the differential geometry.

Our central hypothesis is that there exists a compact set of similarly useful descriptors for the analysis of dynamic 4D surfaces. The primary advantages in considering localised changes are that they provide a naturally useful set of invariant characteristics. We seek a constrained set of terms - a vocabulary - for describing all types of deformation. By using this, we show how to describe what the surface is doing more effectively; and thereby enable better characterisation, and consequently more effective visualisation and comparison.

This thesis investigates this claim. We adopt a bottom-up approach of the problem, in which we acquire raw data from a newly constructed commercial 4D data capture system developed by our industrial partners. A crucial first step resolves the temporal non-linear registration between instances of the captured surface. We employ a combined optical/range flow to guide a conformation over a sequence. By extending the use of aligned colour information alongside the depth data we improve this estimation in the case of local surface motion ambiguities. By employing a KLT/thin-plate-spline method we also seek to preserve global deformation for regions with no estimate.

We then extend aspects of differential geometry theory for existing static surface analysis to the temporal domain. Our initial formulation considers the possible intrinsic transitions from the set of shapes defined by the variations in the magnitudes of the principal curvatures. This gives rise to a total of 15 basic types of deformation. The change in the combined magnitudes also gives an indication of the extent of change. We then extend this to surface characteristics associated with expanding, rotating and shearing; to derive a full set of differential features.

Our experimental results include qualitative assessment of deformations for short episodic registered sequences of both synthetic and real data. The higher-level distinctions extracted are furthermore a useful first step for parsimonious feature extraction, which we then proceed to demonstrate can be used as a basis for further analysis. We ultimately evaluate this approach by considering shape transition features occurring within the human face, and the applicability for identification and expression analysis tasks.