Analysis of Differential and Matching Methods for Optical Flow

Several algorithms for optical flow are studied theoretically and experimentally. Differential and matching methods are examined; these two methods have differing domains of application- differential methods are best when displacements in the image are small (<2 pixels) while matching methods work well for moderate displacements but do not handle sub-pixel motions. Both types of optical flow algorithm can use either local or global constraints, such as spatial smoothness. Local matching and differential techniques and global differential techniques will be examined. Most algorithms for optical flow utilize weak assumptions on the local variation of the flow and on the variation of image brightness. Strengthening these assumptions improves the flow computation. The computational consequence of this is a need for larger spatial and temporal support. Global differential approaches can be extended to local (patchwise) differential methods and local differential methods using higher derivatives. Using larger support is valid when constraint on the local shape of the flow are satisfied. We show that a simple constraint on the local shape of the optical flow, that there is slow spatial variation in the image plane, is often satisfied. We show how local differential methods imply the constraints for related methods using higher derivatives. Experiments show the behavior of these optical flow methods on velocity fields which so not obey the assumptions. Implementation of these methods highlights the importance of numerical differentiation. Numerical approximation of derivatives require care, in two respects: first, it is important that the temporal and spatial derivatives be matched, because of the significant scale differences in space and time, and, second, the derivative estimates improve with larger support.

Shape-Time Photography

We introduce a new method to describe, in a single image, changes in shape over time. We acquire both range and image information with a stationary stereo camera. From the pictures taken, we display a composite image consisting of the image data from the surface closest to the camera at every pixel. This reveals the 3-d relationships over time by easy-to-interpret occlusion relationships in the composite image. We call the composite a shape-time photograph. Small errors in depth measurements cause artifacts in the shape-time images. We correct most of these using a Markov network to estimate the most probable front surface, taking into account the depth measurements, their uncertainties, and layer continuity assumptions.

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.

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.

A Trainable Object Detection System: Car Detection in Static Images

This paper describes a general, trainable architecture for object detection that has previously been applied to face and peoplesdetection with a new application to car detection in static images. Our technique is a learning based approach that uses a set of labeled training data from which an implicit model of an object class -- here, cars -- is learned. Instead of pixel representations that may be noisy and therefore not provide a compact representation for learning, our training images are transformed from pixel space to that of Haar wavelets that respond to local, oriented, multiscale intensity differences. These feature vectors are then used to train a support vector machine classifier. The detection of cars in images is an important step in applications such as traffic monitoring, driver assistance systems, and surveillance, among others. We show several examples of car detection on out-of-sample images and show an ROC curve that highlights the performance of our system.