Mourad Zerroug

Three-dimensional descriptions based on the analysis of the invariant and quasi-invariant properties of some curved-axis generalized cylinders

We address the recovery of object-level 3D descriptions of some classes of curved-axis generalized cylinders. For this, the first part of the paper analyzes the projective properties of two common generic shapes, planar right constant generalized cylinders (PRCGCs) and circular planar right generalized cylinders (circular PRGCs). The properties we analyze include new geometric invariant and quasi-invariant properties of the orthographic projection of the above shapes and a useful classification of their structural properties as functions of their pose. The second part of the paper describes an implemented system which detects and recovers PRCGCs and circular PRGCs from an intensity image in the presence of noise, surface markings, shadows, and partial occlusion. The methods exploit the projective properties to hypothesize and verify relevant curved-axis objects, thus explicitly using the three-dimensionality of the objects and of the desired descriptions. This work extends past work on the recovery of volumetric shapes from an intensity image by addressing new primitives, deriving new properties and by developing a system that recovers them from an intensity image. We demonstrate our method on several real intensity images.

Volumetric descriptions from a single intensity image

Since the early days of computer vision research, shape from contour has been one of the most challenging problems. Many researchers in the field have attempted to understand this problem and proposed different approaches to solve it. Shape from contour still remains one of the hardest problems in the field. The problem has two major difficulties. First, 2D properties of contours of viewed objects are generally not sufficient by themselves to uniquely determine 3D shape, as one dimension is lost in the projection. Second, real images produce imperfect contours that make their interpretation particularly difficult. The first problem has received some attention in the research community but in the context of perfect contours. The second one, however, has received very little.In this work, we propose a promising methodology to address this last problem for a large class of objects: generalized cylinders. It is based on exploiting mathematical invariant properties of the contours of generalized cylinders in a perceptual grouping approach. We show that using these properties greatly helps addressing the figure-ground problem in a more rigorous way than previous (intuitive) perceptual grouping methods. Our approach exploits the interplay between local and global features by handling different levels of the feature hierarchy. We have developed and implemented a method that handles SHGCs in complex seenes with markings and occlusion.We demonstrate the application of our method of shape description and scene segmentation on complex real images. We also demonstrate the usage of the obtained descriptions for recovery of complete 3-D object centered descriptions of viewed objects from a single intensity image.

Quasi-invariant properties and 3-D shape recovery of non-straight, non-constant generalized cylinders

The geometric protective properties of the contours of right generalized cylinders with a planar, but not necessarily straight, axis and circular, but possibly varying in size, cross-sections (called circular PRGCs) are addressed. Important rigourous quasi-invariant properties of circular PRGCs and invariant properties for their subclasses are derived. Their application for 2-D descriptions and for recovery of complete 3-D object-centered descriptions from the 2-D contours is shown.<<ETX>>

Part-based 3D descriptions of complex objects from a single image

Volumetric, 3D, part-based descriptions of complex objects in a scene can be highly beneficial for many tasks such as generic object recognition, navigation, and manipulation. However, it has been difficult to derive such descriptions from image data. There has been some progress in getting such descriptions from range data or from perfect contours, but analysis of a real intensity image presents many difficulties. The object and part boundaries do not completely correspond to image boundaries. The detected boundaries are often fragmented and many boundaries due to surface markings, shadows, and noise are present. In addition, inference of 3D from a 2D image is difficult. The paper describes a method to compute the desired descriptions from a single image by exploiting projective properties of a class of generalized cylinders and of possible joints between them. Experimental results on some examples are given.

Pose estimation of multi-part curved objects

We show that alignment-like techniques can be used for the pose estimation of a large class of structured curved objects. We demonstrate that although it is difficult to isolate distinguished points on the outlines of such objects, high-level descriptions, extracted from a 2D image, based on a part-based formalism using sub-classes of generalized cylinders provide means to establish quasi-invariant correspondences between image and model shapes. We describe the method and show several results on real images.

Using Invariance and Quasi-Invariance for the Segmentation and Recovery of Curved Objects

There has been much interest recently in using invariant theory in computer vision. Most work has concentrated on recognition of 3-D objects from 2-D images using algebraic or differential invariants. In this work, we address the usage of a class of projective invariants and quasi-invariants for the segmentation and 3-D recovery of generalized cylinders from a monocular image. We derive important projective invariants of straight homogeneous generalized cylinders and describe an implemented system for their segmentation and recovery from a monocular intensity image. We then derive quasi-invariant properties of circular planar right generalized cylinders and describe another implemented system for recovering their 3-D shape from 2-D contours. This work shows that the problem of shape description and scene segmentation from a monocular image can be solved for a large class of objects in our environment. Examples of results of both systems are also given.

Segmentation and recovery of SHGCs from a real intensity image

We address the problem of scene segmentation and shape recovery from a single real intensity image. Solving this problem is central to obtaining 3-D scene descriptions in realistic applications where perfect data cannot be obtained and only one image is available. The method we propose addresses a large class of generic shapes, namely straight homogeneous generalized cylinders (SHGCs). It consists of the derivation and use of their geometric projective properties in a multi-level grouping approach. We describe an implemented and working system that detects and recovers full SHGC descriptions in the presence of image imperfections such as broken contours, surface markings, shadows and occlusion. We demonstrate our method on complex real images.

The Challenge of Generic Object Recognition

We discuss the issues and challenges in the development of generic object recognition systems. We argue that high-level, volumetric part-based, descriptions are essential if we want to recognize objects which are similar but not identical to pre-stored models, under wide viewing conditions, and to automatically learn new models and add them to our knowledge base.We discuss the representation scheme and its relationships to the description extraction, recognition and learning processes. We then describe the difficulties in obtaining such descriptions from images and outline steps for robust and efficient implementations. We also demonstrate the viability of the arguments by reporting on recent progress.