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.

Enhanced Reality Visualization in a Surgical Environment

Enhanced reality visualization is the process of enhancing an image by adding to it information which is not present in the original image. A wide variety of information can be added to an image ranging from hidden lines or surfaces to textual or iconic data about a particular part of the image. Enhanced reality visualization is particularly well suited to neurosurgery. By rendering brain structures which are not visible, at the correct location in an image of a patient's head, the surgeon is essentially provided with X-ray vision. He can visualize the spatial relationship between brain structures before he performs a craniotomy and during the surgery he can see what's under the next layer before he cuts through. Given a video image of the patient and a three dimensional model of the patient's brain the problem enhanced reality visualization faces is to render the model from the correct viewpoint and overlay it on the original image. The relationship between the coordinate frames of the patient, the patient's internal anatomy scans and the image plane of the camera observing the patient must be established. This problem is closely related to the camera calibration problem. This report presents a new approach to finding this relationship and develops a system for performing enhanced reality visualization in a surgical environment. Immediately prior to surgery a few circular fiducials are placed near the surgical site. An initial registration of video and internal data is performed using a laser scanner. Following this, our method is fully automatic, runs in nearly real-time, is accurate to within a pixel, allows both patient and camera motion, automatically corrects for changes to the internal camera parameters (focal length, focus, aperture, etc.) and requires only a single image.

Robot Motion Vision by Fixation

In many motion-vision scenarios, a camera (mounted on a moving vehicle) takes images of an environment to find the "motion'' and shape. We introduce a direct-method called fixation for solving this motion-vision problem in its general case. Fixation uses neither feature-correspondence nor optical-flow. Instead, spatio-temporal brightness gradients are used directly. In contrast to previous direct methods, fixation does not restrict the motion or the environment. Moreover, fixation method neither requires tracked images as its input nor uses mechanical tracking for obtaining fixated images. The experimental results on real images are presented and the implementation issues and techniques are discussed.

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.

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.

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.

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.

Learning object segmentation from video data

This memo describes the initial results of a project to create a self-supervised algorithm for learning object segmentation from video data. Developmental psychology and computational experience have demonstrated that the motion segmentation of objects is a simpler, more primitive process than the detection of object boundaries by static image cues. Therefore, motion information provides a plausible supervision signal for learning the static boundary detection task and for evaluating performance on a test set. A video camera and previously developed background subtraction algorithms can automatically produce a large database of motion-segmented images for minimal cost. The purpose of this work is to use the information in such a database to learn how to detect the object boundaries in novel images using static information, such as color, texture, and shape. This work was funded in part by the Office of Naval Research contract #N00014-00-1-0298, in part by the Singapore-MIT Alliance agreement of 11/6/98, and in part by a National Science Foundation Graduate Student Fellowship.

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 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.