Technical Report PHD-2006-08

TR#:PHD-2006-08
Class:PHD
Title: Functional Reasoning in Image Understanding
Authors: Octavian Soldea
Supervisors: Ehud Rivlin and Gershon Elber
PDFPHD-2006-08.pdf
Abstract: We propose a novel scheme for supervised learning function based classification of objects in 3D images. The learning process constructs a generic multi-level hierarchical description of object classes in terms of functional components. The multi-level hierarchy's design and construction involves a large set of signatures based reasoning employing likelihood functions built from histograms as radial-based functions. These signatures consist of geometric properties of shape parts and relationships among them. Initially, the input range data is segmented and each object part is labeled as one of a few possible primitives. Additionally, each group of primitive parts is tagged by a functional symbol. Connections between primitive parts are also computed in the segmentation stage. A probabilistic matching measure is further employed in designing classifiers that are extensively tested.

We use audio based signatures to label parts of the object under analysis. We also propose a novel scheme for fusion between 3D and audio modalities to support function based classification.

We tested the proposed scheme on a database of about one thousand different 3D objects. The results show high accuracy in classification.

Among the geometric properties employed toward classification and evaluated during the construction and use of the multi-level hierarchy we computed geometric properties such as curvatures and moments of 3D and volumetric objects. We also present two results we have obtained in computing curvatures and moments of 3D and volumetric objects.

We present a method to globally segment volumetric images into regions that contain convex or concave (elliptic) iso-surfaces, planar or cylindrical (parabolic) iso-surfaces, and volumetric regions with saddle-like (hyperbolic) iso-surfaces, regardless of the value of the iso-surface level. The proposed scheme relies on a novel approach to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a tri-variate B-spline volumetric representation. This scheme can set the basis for more precise and accurate segmentation of data sets targeting the identification of primitive parts. Since the proposed scheme employs piecewise continuous functions, it is precise and insensitive to aliasing.

A subset of the geometric properties set used in our scheme for classification is moments. In this context, two schemes for computing moments of free-form objects are developed and analyzed. Both schemes take advantage of a representation that is based on the B-spline blending functions.

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