In this work three different analog VLSI motion sensors have been described and characterized. All three sensors were proven to be fully functional. The CMotion1d sensor, the first working sensor to implement the gradient method in 1-D, was shown to compute the 1-D stimulus velocity in real time.  It has been shown that due to the discrete implementation the velocity output becomes dependent on spatial frequency. The Gradient2d sensor uses a gradient based algorithm which allows for a very compact implementation in analog hardware. The combination of small pixel size in a 2-D implementation, desirable motion output for 2-D stimuli and high sensitivity makes this sensor exceptional. Finally the FTC sensor, which implements a feature based algorithm, was able to generate rather complex flow fields with just direction-of-motion information.

All three sensors share in common that they combine imaging and computation on one single chip. The entire motion detection system therefore consists of only the sensor chip, a lens, some potentiometers to supply the bias voltages and an operational amplifier to amplify the sensor output currents.  A conclusive comparison between these sensors is not possible without a specific application in mind. Generally all of the sensors could be used where compactness, low mass, low power consumption, high speed, robustness against mechanical stress or a low price is needed. This could be in mobile robotics, in cars, in portable electronics and real time applications.

Analog VLSI motion sensors of the kind presented in this work could also be used in a very different context. Computer software models of biological vision systems can be very flexible and have been developed extensively in the past. For complex models, though, simulation times can become long. Additionally natural images are not usually used as input to the simulations. Analog VLSI implementations of models of vision systems could be used favorably in this context, because their operation is in real time, natural images can be captured, and their architecture is inherently parallel already. In particular with the motion sensors described in this thesis not only the motion information is available, but also the input image, so that sensory fusion might be investigated.

In the following the individual strengths and weaknesses of the sensors are summarized, and possible applications are proposed.

The CMotion1d sensor and a possible 2-D implementation of the gradient method are fascinating demonstrations of how mathematical operations can be performed in analog VLSI. An algorithm has been derived that could equally well be used in a machine vision computer application, and was straightforwardly implemented in hardware. This approach yielded a sensor which is capable of computing the true stimulus velocity, but at the cost of a larger pixel.  The strengths of the CMotion1d sensor are:

- Continuous time velocity computation, as compared to sample-and-hold type sensors

- Velocity output independent of contrast down to 20% contrast

- Direction selectivity maintained down to 4% contrast

- Single pixel velocity output approximately linear to stimulus velocity over a range of three orders of magnitude (measured from 0.072 mm/sec to 76 mm/sec)

- Velocity output almost linear to rotational velocity up to measured stimulus speeds of 353 rpm

whereas the following undesired properties of the CMotion1d sensor have been found:

- Large pixel size (147 mu m x 270 mu m in 2.0 mu m technology for 1-D sensor, 292 mu m x 292 mu m in 2.0 mu m technology for 2-D sensor

- Spatial frequency dependence (predicted by the gradient method for a discrete spatial derivative)

- Divergent velocity output for stimulus directions close to +-90 degree (predicted by the gradient method, not due to the hardware implementation)

The CMotion1d sensor is suited for applications where a velocity signal is required, high speeds can occur and the input signal is approximately 1-D.

The Gradient2d sensor has been proven to be the most robust of all three presented sensors. Few biases are required and none of them is overly sensitive. The pixel size is very small due to the algorithm, which was developed specifically for a hardware implementation. In summary the advantages of this sensor are:

- Very small pixel size (217 mu m x 210 mu m in 2.0 mu m technology, 112 mu m x 112 mu m in 1.2 mu m technology)

- Motion output monotonic with stimulus velocity (measured from 0.05 mm/sec to 76 mm/sec)

- High sensitivity to low contrast stimuli. Direction selectivity maintained down to 2% contrast

- Desirable orientation tuning curve, suited for 2-D operation (cosine shaped for not too high contrast stimuli)

- Few bias voltages required. No critical adjustments required

The following features could be seen as drawbacks of the Gradient2d sensor

- Time dependent motion output. If a more stable motion output is desired, it can be averaged over a short time

- Motion output dependent on contrast and spatial frequency. The dependency is such that the motion output degrades gracefully towards small contrasts and spatial frequencies and towards the aliasing point

The Gradient2d sensor is the most promising sensor if a high density array of direction of motion cells is desired. The sensor not only reports direction-of-motion continuously in angular space, but the length of the motion vectors additionally codes for the stimulus speed.

The FTC sensor was shown to compute rather complex direction-of-motion flow fields on a 12 x 13 pixel array. The motion output of every pixel is held on chip for a programmable time, which can be useful for some applications. The FTC sensor features the following properties:

- Small pixel size (119 mu m x 128 mu m in 1.2 mu m technology)

- Direction-of-motion detected correctly over a wide velocity range (90% confidence for high contrast stimuli for speeds from 0.5 pixels/sec to 500 pixels/sec)

- Good contrast sensitivity (90% confidence down to 20% contrast)

- Programmable persistence time

Problem areas with the FTC sensor are

- Angular resolution only +-45 degree

- Temporal edge detector is crucial for sensor performance (sensitivity, spike length and independency of stimulus shape)

- Critical biases in the temporal edge detector (threshold, TED bias and gain)

The FTC sensor might be used favorably for problem classes, where only the direction of motion field is required. Scalar parameters, like the focus-of-expansion, the focus-of-contraction, the axis-of-rotation, the direction of rotation, the overall direction-of-motion could be recovered from a direction-of-motion field. Additionally the FTC sensor might be used in sensory motor systems, where a feedback signal is required, that is derived from a moving scene. The FTC scheme could be improved to compute velocity, which would make this sensor even more versatile.

In summary, with the motion sensors presented in this work it has been proven, that
(a) both correlation based and gradient based methods for motion computation can successfully be implemented in analog VLSI, and
(b) high density 2-D motion sensors can be built.