Visual Tracking

A typical robot vision scenario might involve a vehicle moving with an unknown 3D motion (translation and rotation) while taking intensity images of an arbitrary environment. This paper describes the theory and implementation issues of tracking any desired point in the environment. This method is performed completely in software without any need to mechanically move the camera relative to the vehicle. This tracking technique is simple an inexpensive. Furthermore, it does not use either optical flow or feature correspondence. Instead, the spatio-temporal gradients of the input intensity images are used directly. The experimental results presented support the idea of tracking in software. The final result is a sequence of tracked images where the desired point is kept stationary in the images independent of the nature of the relative motion. Finally, the quality of these tracked images are examined using spatio-temporal gradient maps.

An Analog VLSI Chip for Estimating the Focus of Expansion

For applications involving the control of moving vehicles, the recovery of relative motion between a camera and its environment is of high utility. This thesis describes the design and testing of a real-time analog VLSI chip which estimates the focus of expansion (FOE) from measured time-varying images. Our approach assumes a camera moving through a fixed world with translational velocity; the FOE is the projection of the translation vector onto the image plane. This location is the point towards which the camera is moving, and other points appear to be expanding outward from. By way of the camera imaging parameters, the location of the FOE gives the direction of 3-D translation. The algorithm we use for estimating the FOE minimizes the sum of squares of the differences at every pixel between the observed time variation of brightness and the predicted variation given the assumed position of the FOE. This minimization is not straightforward, because the relationship between the brightness derivatives depends on the unknown distance to the surface being imaged. However, image points where brightness is instantaneously constant play a critical role. Ideally, the FOE would be at the intersection of the tangents to the iso-brightness contours at these "stationary" points. In practice, brightness derivatives are hard to estimate accurately given that the image is quite noisy. Reliable results can nevertheless be obtained if the image contains many stationary points and the point is found that minimizes the sum of squares of the perpendicular distances from the tangents at the stationary points. The FOE chip calculates the gradient of this least-squares minimization sum, and the estimation is performed by closing a feedback loop around it. The chip has been implemented using an embedded CCD imager for image acquisition and a row-parallel processing scheme. A 64 x 64 version was fabricated in a 2um CCD/ BiCMOS process through MOSIS with a design goal of 200 mW of on-chip power, a top frame rate of 1000 frames/second, and a basic accuracy of 5%. A complete experimental system which estimates the FOE in real time using real motion and image scenes is demonstrated.

The Perceptual Buildup of Three-Dimensional Structure from Motion

We present psychophysical experiments that measure the accuracy of perceived 3D structure derived from relative image motion. The experiments are motivated by Ullman's incremental rigidity scheme, which builds up 3D structure incrementally over an extended time. Our main conclusions are: first, the human system derives an accurate model of the relative depths of moving points, even in the presence of noise; second, the accuracy of 3D structure improves with time, eventually reaching a plateau; and third, the 3D structure currently perceived depends on previous 3D models. Through computer simulations, we relate the psychophysical observations to the behavior of Ullman's model.

Recovering Three-Dimensional Structure from Motion with Surface Reconstruction

We address the computational role that the construction of a complete surface representation may play in the recovery of 3--D structure from motion. We present a model that combines a feature--based structure--from- -motion algorithm with smooth surface interpolation. This model can represent multiple surfaces in a given viewing direction, incorporates surface constraints from object boundaries, and groups image features using their 2--D image motion. Computer simulations relate the model's behavior to perceptual observations. In a companion paper, we discuss further perceptual experiments regarding the role of surface reconstruction in the human recovery of 3--D structure from motion.

Towards Autonomous Motion Vision

Earlier, we introduced a direct method called fixation for the recovery of shape and motion in the general case. The method uses neither feature correspondence nor optical flow. Instead, it directly employs the spatiotemporal gradients of image brightness. This work reports the experimental results of applying some of our fixation algorithms to a sequence of real images where the motion is a combination of translation and rotation. These results show that parameters such as the fization patch size have crucial effects on the estimation of some motion parameters. Some of the critical issues involved in the implementaion of our autonomous motion vision system are also discussed here. Among those are the criteria for automatic choice of an optimum size for the fixation patch, and an appropriate location for the fixation point which result in good estimates for important motion parameters. Finally, a calibration method is described for identifying the real location of the rotation axis in imaging systems.

Pattern Motion Perception: Feature Tracking or Integration of Component Motions?

A key question regarding primate visual motion perception is whether the motion of 2D patterns is recovered by tracking distinctive localizable features [Lorenceau and Gorea, 1989; Rubin and Hochstein, 1992] or by integrating ambiguous local motion estimates [Adelson and Movshon, 1982; Wilson and Kim, 1992]. For a two-grating plaid pattern, this translates to either tracking the grating intersections or to appropriately combining the motion estimates for each grating. Since both component and feature information are simultaneously available in any plaid pattern made of contrast defined gratings, it is unclear how to determine which of the two schemes is actually used to recover the plaid"s motion. To address this problem, we have designed a plaid pattern made with subjective, rather than contrast defined, gratings. The distinguishing characteristic of such a plaid pattern is that it contains no contrast defined intersections that may be tracked. We find that notwithstanding the absence of such features, observers can accurately recover the pattern velocity. Additionally we show that the hypothesis of tracking "illusory features" to estimate pattern motion does not stand up to experimental test. These results present direct evidence in support of the idea that calls for the integration of component motions over the one that mandates tracking localized features to recover 2D pattern motion. The localized features, we suggest, are used primarily as providers of grouping information - which component motion signals to integrate and which not to.

Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call "relative affine structure". Via a number of corollaries of our main results we show that our framework unifies previous work --- including Euclidean, projective and affine --- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.

Learning Fine Motion by Markov Mixtures of Experts

Compliant control is a standard method for performing fine manipulation tasks, like grasping and assembly, but it requires estimation of the state of contact between the robot arm and the objects involved. Here we present a method to learn a model of the movement from measured data. The method requires little or no prior knowledge and the resulting model explicitly estimates the state of contact. The current state of contact is viewed as the hidden state variable of a discrete HMM. The control dependent transition probabilities between states are modeled as parametrized functions of the measurement We show that their parameters can be estimated from measurements concurrently with the estimation of the parameters of the movement in each state of contact. The learning algorithm is a variant of the EM procedure. The E step is computed exactly; solving the M step exactly would require solving a set of coupled nonlinear algebraic equations in the parameters. Instead, gradient ascent is used to produce an increase in likelihood.

Direct Estimation of Motion and Extended Scene Structure from a Moving Stereo Rig

We describe a new method for motion estimation and 3D reconstruction from stereo image sequences obtained by a stereo rig moving through a rigid world. We show that given two stereo pairs one can compute the motion of the stereo rig directly from the image derivatives (spatial and temporal). Correspondences are not required. One can then use the images from both pairs combined to compute a dense depth map. The motion estimates between stereo pairs enable us to combine depth maps from all the pairs in the sequence to form an extended scene reconstruction and we show results from a real image sequence. The motion computation is a linear least squares computation using all the pixels in the image. Areas with little or no contrast are implicitly weighted less so one does not have to explicitly apply a confidence measure.

Structure from Stereo and Motion

Stereopsis and motion parallax are two methods for recovering three dimensional shape. Theoretical analyses of each method show that neither alone can recover rigid 3D shapes correctly unless other information, such as perspective, is included. The solutions for recovering rigid structure from motion have a reflection ambiguity; the depth scale of the stereoscopic solution will not be known unless the fixation distance is specified in units of interpupil separation. (Hence the configuration will appear distorted.) However, the correct configuration and the disposition of a rigid 3D shape can be recovered if stereopsis and motion are integrated, for then a unique solution follows from a set of linear equations. The correct interpretation requires only three points and two stereo views.

Computing 3-D Motion in Custom Analog and Digital VLSI

This thesis examines a complete design framework for a real-time, autonomous system with specialized VLSI hardware for computing 3-D camera motion. In the proposed architecture, the first step is to determine point correspondences between two images. Two processors, a CCD array edge detector and a mixed analog/digital binary block correlator, are proposed for this task. The report is divided into three parts. Part I covers the algorithmic analysis; part II describes the design and test of a 32$\time $32 CCD edge detector fabricated through MOSIS; and part III compares the design of the mixed analog/digital correlator to a fully digital implementation.

Temporal Surface Reconstruction

This thesis investigates the problem of estimating the three-dimensional structure of a scene from a sequence of images. Structure information is recovered from images continuously using shading, motion or other visual mechanisms. A Kalman filter represents structure in a dense depth map. With each new image, the filter first updates the current depth map by a minimum variance estimate that best fits the new image data and the previous estimate. Then the structure estimate is predicted for the next time step by a transformation that accounts for relative camera motion. Experimental evaluation shows the significant improvement in quality and computation time that can be achieved using this technique.

The Early Detection of Motion Boundaries

This thesis shows how to detect boundaries on the basis of motion information alone. The detection is performed in two stages: (i) the local estimation of motion discontinuities and of the visual flowsfield; (ii) the extraction of complete boundaries belonging to differently moving objects. For the first stage, three new methods are presented: the "Bimodality Tests,'' the "Bi-distribution Test,'' and the "Dynamic Occlusion Method.'' The second stage consists of applying the "Structural Saliency Method,'' by Sha'ashua and Ullman to extract complete and unique boundaries from the output of the first stage. The developed methods can successfully segment complex motion sequences.

Error Detection and Recovery for Robot Motion Planning with Uncertainty

Robots must plan and execute tasks in the presence of uncertainty. Uncertainty arises from sensing errors, control errors, and uncertainty in the geometry of the environment. The last, which is called model error, has received little previous attention. We present a framework for computing motion strategies that are guaranteed to succeed in the presence of all three kinds of uncertainty. The motion strategies comprise sensor-based gross motions, compliant motions, and simple pushing motions.

Planning and Teaching Compliant Motion Strategies

This thesis presents a new high level robot programming system. The programming system can be used to construct strategies consisting of compliant motions, in which a moving robot slides along obstacles in its environment. The programming system is referred to as high level because the user is spared of many robot-level details, such as the specification of conditional tests, motion termination conditions, and compliance parameters. Instead, the user specifies task-level information, including a geometric model of the robot and its environment. The user may also have to specify some suggested motions. There are two main system components. The first component is an interactive teaching system which accepts motion commands from a user and attempts to build a compliant motion strategy using the specified motions as building blocks. The second component is an autonomous compliant motion planner, which is intended to spare the user from dealing with "simple" problems. The planner simplifies the representation of the environment by decomposing the configuration space of the robot into a finite state space, whose states are vertices, edges, faces, and combinations thereof. States are inked to each other by arcs, which represent reliable compliant motions. Using best first search, states are expanded until a strategy is found from the start state to a global state. This component represents one of the first implemented compliant motion planners. The programming system has been implemented on a Symbolics 3600 computer, and tested on several examples. One of the resulting compliant motion strategies was successfully executed on an IBM 7565 robot manipulator.