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`
`© Copyright 1992
`by Benjamin B. Bederson
`All Rights Reserved
`
`Page 2 of 86
`
`

`

`Abstract
`
`Wehavedeveloped a prototype miniaturized active vision system whose sensor architecture is based on
`a logarithmically structured space-variant pixel geometry. A space-variant image’s resolution changes
`across the image. Typically, the central part of the image has a very high resolution, and the resolution
`falls off gradually in the periphery. Our system integrates a miniature CCD-based camera, pan-tilt
`actuator, controller, general purpose processors and display. Due to the ability of space-variant sensors
`to cover large work-spaces, yet provide high acuity with an extremely small number of pixels, space-
`variant active vision system architectures provide the potential for radical reductions in system size and
`cost. We haverealized this by creating an entire system that takes up less than a third of a cubic foot.
`In this thesis, we describe a prototype space-variant active vision system (Cortex-I) which performs
`such tasks as tracking moving objects and license plate reading, and functions as a video telephone.
`Wereport on the design and construction of the camera (which is 8 x 8 x 8mm), its readout, and
`a fast mapping algorithm to convert the uniform image to a space-variant image. We introduce a new
`miniature pan-tilt actuator, the Spherical Pointing Motor (SPM), which is 4 x 5 x 6cm. The basic idea
`behind the SPMis to orient a permanent magnet to the magnetic field induced by three orthogonal coils
`by applying the appropriate ratio of currents to the coils. Finally, we present results of integrating the
`system with several applications. Potential application domains for systems of this type include vision
`systems for mobile robots and robot manipulators, traffic monitoring systems, security and surveillance,
`telerobotics, and consumer video communications.
`The long-range goal of this project is to demonstrate that major new applications of robotics will
`become feasible when small low-cost machine vision systems can be mass-produced. This notion of
`“commodity robotics” is expected to parallel the impact of the personal computer, in the sense of opening
`up new application niches for what has until now been expensive and therefore limited technology.
`
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`
`Page 3 of 86
`
`iti
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`

`Acknowledgements
`
`This work is the result of a collaborative effort. It was a pleasure to have had the opportunity to work
`with such fine minds as I found in Eric Schwartz (my thesis advisor), Richard Wallace (my colleague
`and constant teacher), and Ping-Wen Ong (my fellow student and supporter).
`Eric has been doing research leading up to this project for at least ten years. He found the funding
`for it, and had manyof the critical ideas that got it moving. The Spherical Pointing Motor was his
`original idea, and only through(literally) years of bouncing it off each other, did we get it right.
`Richard is largely responsible for the digital signal processing in the system. If it weren’t for him,
`we wouldn’t have a video display. He had infinite patience in helping me work through problems. He
`was always available to assist me, and helped to keep the project well directed.
`Ping-wen came through at the last minute to integrate his license plate tracking software to work
`with Cortex-I.
`In addition, he was a motivating force in my studying Chinese. While not directly
`critical to this project, studying Chinese helped me keep my sanity during various traumas — such as
`when thefirst prototype went flying through the air as I got a great electric shock — a few hours before
`we departed for Chicago where Cortex-I wasfirst publicly demonstrated.
`Everyone at the NYU Robotics Lab was always optimistic and supportive as Cortex-I slowly took
`shape. Bud Mishra, especially, had good ideas, and was kind enough to read this thesis twice.
`Andof course, I thank my family, friends, and cat (Tria) who have had to put up with me as I’ve
`been counting down the monthsto finish this, and start the next phase of mylife.
`
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`
`

`

`

`CHAPTER 1.
`
`INTRODUCTION
`
`2
`
`1. Saccades: These are discrete movements and movethe eye quickly (300° - 400°/second) from one
`fixation point to another. They also correct errors of the pursuit system. There is a large latency
`(150 ms) between fixations. There are typically less than four saccades per second.
`
`2. Pursuit Eye Movements: The pursuit system tracks moving targets and keeps the current
`target foveated. It has a latency of 50ms.
`
`3. Vergence: This controls the depth that the two eyes fixate on together. It is the slowest system
`and has a latency of over 200ms.
`
`resolution. It does so with the use of the retina, which is a space-variant sensor. It has a resolution that
`is high in the center (called the fovea), low in the periphery and it changes smoothly between them.
`Any system that uses a space-variant sensor must aim the sensor properly. Since space-variant sensors
`only have high resolution in the fovea, the current region of interest must be continuously tracked or
`foveated. Such a sensor must be mounted in a device that can aim the sensor with precision. A system
`with this capability is an example of an active or attentive vision system.
`A logmap sensoris a useful type of space-variant sensor that is modelled on the human visual system
`(see Section 1.3). The space complexity aspect of logmap sensors is particularly attractive and has
`been analyzed in detail [7].
`In this work, a spatial quality measure, Q;, for sensors is defined to be
`the ratio of its work-space to maximal resolution. Logmap sensors can each achieve comparable Q, to
`conventional uniform sensors that are one to four orders of magnitude larger. Image simulation of the
`human space-variant architecture suggests that this ratio may be as high as 10,000: 1 [7]. In current
`implementations of space-variant machine vision systems, logmap sensors with between 1000 and 2000
`pixels have comparable Q, to conventional sensors in the range of 256 x 256 to 512 x 512, a compression
`of between 60 : 1 to 250 : 1. Moreover, as shown in [?], Q, grows exponentially with the number of
`pixels in the logmap sensor, thus providing a highly favorable route to upgrading sensor quality. The
`high compression ratios cited above for the human visual system derive from the fact that human acuity,
`which is roughly one-arc minute in the fovea, when extrapolated over a 120 degree visual field, yields
`a constant resolution sensor with roughly 0.2 gigapixels. The logmap sensor with comparable Q, has
`roughly 10* to 10° pixels.
`In this discussion, compression refers to the ratio of the numberof pixels in a conventional uniform
`sensor to that of a space-variant sensor with the same @),. The issue of image compression,
`in the
`conventional (e.g. JPEG) usage is an independent issue not addressed in this thesis, but we point out
`that a form of progressive video coding, in which a video image is represented by a sequence of logmap
`images, is one application that has benefitted from the high compressionratio of the logmap transform. If
`each logmap image is centered on a different point in the video image and clipped so that we preserve the
`highest frequency information available at each point in the video picture, we can progressively construct
`a video image of increasing detail. Rojer [?] reported some experiments with progressive logmap video
`coding, and discussed the problem of selecting the best sequence of gaze points.
`If the sensor is not
`A space-variant sensor requires pointing the sensor at the region of interest.
`pointed (or foveated) properly, the desired object will fall somewhere on the periphery of the sensor
`resulting in a lower resolution image. So it is important to develop efficient eye movement mechanisms.
`A sensor movement system mustfind interesting objects, track them as they move, and account for
`movement of the device the sensor is mounted in. A short description of the way the human system
`solves the second two parts of this problem follows. It should be noted that the human visual system
`is able to track objects and foveate on them to within the accuracy of the retina’s highest resolution.
`There are four principal types of eye movements as reviewed by Robinson [?].
`
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`
`4. Vestibular Systems: The Vestibular Ocular Reflex and Optokinetic Reflex systems maintain
`the gaze of the eye, counteracting for head movements.
`I.e., if the head moves to the right, the
`eye movesto the left. This is one of the fastest types of eye movement and hasa latency of only
`14ms. These get sensory input from the semicircular canals that effectively constitute an angular
`inertial accelerometer with a frequency range from 0.017 to 17Hz.
`
`Page 8 of 86
`
`

`

`Substituting
`
`we get
`
`or,
`
`log(re®”) = logr + i0
`
`g=logr
`
`and y=8@,
`
`;
`log(re®) = x + iy
`
`log(P,) = P..
`
`CHAPTER 1.
`
`INTRODUCTION
`
`3
`
`In addition to these four systems,there is a fifth type of movement known as physiological nystagmus.
`This is a small higher frequency jitter at 30 to 80Hz. These movements are very important to the low-
`level visual process, but are not an issue in the larger movements of object tracking with which we are
`concerned here.
`In our work, we focus on saccadic motions which are the simplest to implement and are used for both
`attention and tracking.
`The mappingof the retina to the visual cortex is another very important characteristic of the human
`visual system. Pioneering work by Hubel and Wiesel [?, ?] showed how some low-level feature detection
`performed on the retinal image was mapped to the V1 area in the visual cortex. Then Schwartz showed
`in [?, ?] that the mapping from the retina to the visual cortex takes a very specialized form. Specifically,
`the retina can be looked at as a polar coordinate system where each point represents one photo-sensitive
`cell. It gets mapped to what is essentially a rectangular coordinate system in the visual cortex. This
`can be represented mathematically by a complex logarithm and is depicted graphically in Figure 1.1.
`This mappingis called the logmap.
`The point in retinal space, P,, can be denoted re’ and the point in cortical space, P,, can be denoted
`by the complex number z + iy. If we take the log of P,, we get:
`
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