Algebraic Functions For Recognition

In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment --- yielding a direct method that cuts through the computations of camera transformation, scene structure and epipolar geometry. The proof of the central result may be of further interest as it demonstrates certain regularities across homographies of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in re-projection tasks.

Extracting Salient Curves from Images: An Analysis of the Saliency Network

The Saliency Network proposed by Shashua and Ullman is a well-known approach to the problem of extracting salient curves from images while performing gap completion. This paper analyzes the Saliency Network. The Saliency Network is attractive for several reasons. First, the network generally prefers long and smooth curves over short or wiggly ones. While computing saliencies, the network also fills in gaps with smooth completions and tolerates noise. Finally, the network is locally connected, and its size is proportional to the size of the image. Nevertheless, our analysis reveals certain weaknesses with the method. In particular, we show cases in which the most salient element does not lie on the perceptually most salient curve. Furthermore, in some cases the saliency measure changes its preferences when curves are scaled uniformly. Also, we show that for certain fragmented curves the measure prefers large gaps over a few small gaps of the same total size. In addition, we analyze the time complexity required by the method. We show that the number of steps required for convergence in serial implementations is quadratic in the size of the network, and in parallel implementations is linear in the size of the network. We discuss problems due to coarse sampling of the range of possible orientations. We show that with proper sampling the complexity of the network becomes cubic in the size of the network. Finally, we consider the possibility of using the Saliency Network for grouping. We show that the Saliency Network recovers the most salient curve efficiently, but it has problems with identifying any salient curve other than the most salient one.

The Synthesis of Stable Grasps in the Plane

This paper addresses the problem of synthesizing stable grasps on arbitrary planar polygons. Each finger is a virtual spring whose stiffnes and compression can be programmed. The contacts between the finger tips and the object are point contacts without friction. We prove that all force-closure grasps can be made stable, and it costs 0(n) time to synthesize a set of n virtual springs such that a given force closure grasp is stable. We can also choose the compliance center and the stiffness matrix of the grasp, and so choose the compliant behavior of the grasped object about its equilibrium. The planning and execution of grasps and assembly operations become easier and less sensitive to errors.

Shape from Shading: A Method for Obtaining the Shape of a Smooth Opaque Object from One View

A method will be described for finding the shape of a smooth apaque object form a monocular image, given a knowledge of the surface photometry, the position of the lightsource and certain auxiliary information to resolve ambiguities. This method is complementary to the use of stereoscopy which relies on matching up sharp detail and will fail on smooth objects. Until now the image processing of single views has been restricted to objects which can meaningfully be considered two-dimensional or bounded by plane surfaces. It is possible to derive a first-order non-linear partial differential equation in two unknowns relating the intensity at the image points to the shape of the objects. This equation can be solved by means of an equivalent set of five ordinary differential equations. A curve traced out by solving this set of equations for one set of starting values is called a characteristic strip. Starting one of these strips from each point on some initial curve will produce the whole solution surface. The initial curves can usually be constructed around so-called singular points. A number of applications of this metod will be discussed including one to lunar topography and one to the scanning electron microscope. In both of these cases great simplifications occur in the equations. A note on polyhedra follows and a quantitative theory of facial make-up is touched upon. An implementation of some of these ideas on the PDP-6 computer with its attached image-dissector camera at the Artificial intelligence Laboratory will be described, and also a nose-recognition program.

Image Based Rendering Using Algebraic Techniques

This paper presents an image-based rendering system using algebraic relations between different views of an object. The system uses pictures of an object taken from known positions. Given three such images it can generate "virtual'' ones as the object would look from any position near the ones that the two input images were taken from. The extrapolation from the example images can be up to about 60 degrees of rotation. The system is based on the trilinear constraints that bind any three view so fan object. As a side result, we propose two new methods for camera calibration. We developed and used one of them. We implemented the system and tested it on real images of objects and faces. We also show experimentally that even when only two images taken from unknown positions are given, the system can be used to render the object from other view points as long as we have a good estimate of the internal parameters of the camera used and we are able to find good correspondence between the example images. In addition, we present the relation between these algebraic constraints and a factorization method for shape and motion estimation. As a result we propose a method for motion estimation in the special case of orthographic projection.

Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views

We investigate the differences --- conceptually and algorithmically --- between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. We then use the affine invariant to derive new algebraic connections between perspective views. It is shown that three perspective views of an object are connected by certain algebraic functions of image coordinates alone (no structure or camera geometry needs to be involved).