Applying the identified themes in an instrument: Developing the instrument I put together a construct of participants' perceptions to develop a questionnaire or an

the appropriate lter bandwidth using only gradient information. By combining explicit matching and dierential methods, however, it should be possible to devise a reliable sys-tem which takes advantage of the best of each. Explicit matching methods can determine the maximum image displacements and compute the motion parameters, while dieren-tial methods can more easily obtain information that relates motion and structure from all parts of the image. For example, given the motion and assuming the image has been appropriately lowpass-ltered, depth can be computed from equation (2.56) as

Z

=^;

s

b

E

^t+ (

v

^!b)

⁽²

:

74) In this thesis we are primarily concerned with the design of a system to compute relative motion from explicit point correspondences and will not explore further the benets, or the details, of interfacing to other systems based on dierent approaches. It should be understood, however, that the choice of an explicit strategy does not rule out its use in conjunction with other methods.

image plane. In this case the error function (2.55) to be minimized reduces to

_2tot =^{Z Z} (

E

x

u

+

E

y

v

+

E

t)²

dxdy

(2

:

75) Since the ow is constant, the problem is solved by taking derivatives with respect to

u

and

v

and setting these to zero. We nd that

d

_2tot

du

⁼

Z Z

(

E

x

u

+

E

y

v

+

E

t)

E

x

dxdy

(2.76)

d

_2tot

dv

⁼

Z Z

(

E

x

u

+

E

y

v

+

E

t)

E

x

dxdy

(2.77) In the gradient descent approach, currents proportional to quantities in the integrals are fed into a negative feedback loop which drives the variable voltages representing

u

and

v

to values which force the derivatives to zero. This circuit was designed to operate in continuous time to avoid temporal aliasing. The rst chip built was an 88 array with processors at each pixel to compute the local multiplications and two global busses to carry the values of

u

and

v

.

Other circuits developed by the Computation and Neural Systems Program group at CalTech are described by Horiuchi et al. in [56] where they discuss a comparative study of four experimental designs for 1-D motion estimation. Among these were a 1-D version of Tanner's gradient descent optical ow chip and a fully digital circuit composed of o-the-shelf components to implement correlation. The other two designs were a pulse-coded correlation circuit (based on a model of structures found in the auditory system of owls) which detects time dierences between neighboring pulses, and a mixed analog/digital sys-tem to track zero-crossings of a dierence of Gaussians (DOG) ltered image. In their results, they report that the fully digital circuit, composed of a Fairchild Linear CCD 256 pixel array and a Harris RTX2001A microprocessor, had the best performance in overall robustness, while the Tanner 1-D optical ow chip had the least reliable performance. They also reported diculties using gradient methods due to the 120Hz icker found in ordinary room lights.

There has been a great deal of interest, motivated by the desire to reduce interchip communication requirements, in developing one-chip circuits that incorporate photosensing and local processing at each pixel [57]. With focal-plane processing, however, the area taken up by the processing circuitry increases pixel size and therby reduces the maximum array

size which can be placed on the chip. Since technology limitations restrict the maximum die size to about 1cm², either resolution or eld of view must be sacriced.

Gottardi and Yang [58] recently reported the development of a single chip 1-D motion sensor in CCD/CMOS technology with a 115-pixel linear image sensor and CCD charge subtraction circuits to perform correlation. McQuirk is currently working on a one-chip design for a focus of expansion (FOE) detector using the direct approach developed by Negahdaripour and Horn [45]. The system architecture and results of a preliminary test chip are reported in [59]. In order to obtain a reasonable array size (6464 in 2

technology), McQuirk chose not to implement a fully parallel processor array, but to time-multiplex the computation using one processor per column. Instead of the continuous-time gradient descent method performed by Tanner's optical ow chip, this system computes a discrete-time iterative approximation to minimize the associated error function. Results from the nal design of the complete 6464 array chip are not yet available.

The common feature of the above systems is that they deal with only a very limited aspect of the problem. Most assume constant optical ow, and none allow for rotation.

Given current technology limitations and the complexity of computing general motion, it is probably safe to conclude that it cannot be done with a single chip design at any time in the forseeable future. One reason for designing simpler subsystems is so that they can be combined to solve more complex problems. As yet, however, no one has built or proposed a complete system which includes the design of specialized processors for computing general motion, or relative orientation, in unrestricted environments.

This is the problem which is addressed in this thesis.

Matching Points in Images

Having chosen to build the system based on an explicit matching approach, we must now determine the approach for nding the point correspondences. There are several reasons why obtaining accurate and reliable point correspondences is a hard problem. One is that the same features in two dierent images do not necessarily look the same due to dierences in foreshortening. Features which appear in one image may be occluded or outside the eld of view in the other, or there may be multiple solutions for matching if there are repeating patterns in the images. The high computational cost of computing similarity measures is an additional drawback to obtaining a large number of accurate matches.

Methods which have been proposed for determining correspondences can be grouped into three broad categories: brightness-based methods, gray-level correlation, and edge-based methods. These dier primarily in the types of features used and in their strategy for solving the problem. Hybrid methods, which combine aspects from each of the approaches, have also been developed; however, these are best understood by examining the major categories individually. In this chapter, I will review the advantages and weaknesses of the dierent approaches and discuss their practicality for hardware implementation with respect to the goals of the present system.

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