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.

Internal Camera Calibration Using Rotation and Geometric Shapes

This paper describes a simple method for internal camera calibration for computer vision. This method is based on tracking image features through a sequence of images while the camera undergoes pure rotation. The location of the features relative to the camera or to each other need not be known and therefore this method can be used both for laboratory calibration and for self calibration in autonomous robots working in unstructured environments. A second method of calibration is also presented. This method uses simple geometric objects such as spheres and straight lines to The camera parameters. Calibration is performed using both methods and the results compared.

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.

Monitoring Activities from Multiple Video Streams: Establishing a Common Coordinate Frame

Passive monitoring of large sites typically requires coordination between multiple cameras, which in turn requires methods for automatically relating events between distributed cameras. This paper tackles the problem of self-calibration of multiple cameras which are very far apart, using feature correspondences to determine the camera geometry. The key problem is finding such correspondences. Since the camera geometry and photometric characteristics vary considerably between images, one cannot use brightness and/or proximity constraints. Instead we apply planar geometric constraints to moving objects in the scene in order to align the scene"s ground plane across multiple views. We do not assume synchronized cameras, and we show that enforcing geometric constraints enables us to align the tracking data in time. Once we have recovered the homography which aligns the planar structure in the scene, we can compute from the homography matrix the 3D position of the plane and the relative camera positions. This in turn enables us to recover a homography matrix which maps the images to an overhead view. We demonstrate this technique in two settings: a controlled lab setting where we test the effects of errors in internal camera calibration, and an uncontrolled, outdoor setting in which the full procedure is applied to external camera calibration and ground plane recovery. In spite of noise in the internal camera parameters and image data, the system successfully recovers both planar structure and relative camera positions in both settings.

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.

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.

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.

The Role of Fixation and Visual Attention in Object Recognition

This research project is a study of the role of fixation and visual attention in object recognition. In this project, we build an active vision system which can recognize a target object in a cluttered scene efficiently and reliably. Our system integrates visual cues like color and stereo to perform figure/ground separation, yielding candidate regions on which to focus attention. Within each image region, we use stereo to extract features that lie within a narrow disparity range about the fixation position. These selected features are then used as input to an alignment-style recognition system. We show that visual attention and fixation significantly reduce the complexity and the false identifications in model-based recognition using Alignment methods. We also demonstrate that stereo can be used effectively as a figure/ground separator without the need for accurate camera calibration.

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.