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Chapter 4

In this chapter a high-accuracy light-str'pe vision stem is presented and some mechanisms which generate errors in measuring part positions are analyzed. Errors may be generated from the discrete nature of sensors inaccuracies in part, models, errors in the calibration procedures, inaccurate sensor system model, and system parameter variations due to changing environmental conditions. Quantization er-rors are analyzed and some techniques for 'improving measurement accuracy are developed as a result of the analysis.

4.1 Lterature Review of Feature Extraction Techniques

106 Chapter 4 Feature Localization Using a Lght Stripe Vision System

of literature which sometimes concerns itself with accuracy issues 'is the edge and

feature detection literature 40,41,49,92,118,121]. MacVicar and Binford 118] claim subpixel edge detection accuracy for a modified Binford-Horn detector although no data is presented. Canny 40,41] derive 's an edge detector operator which is optimal with respect to three performance criterion:

Good detection. There sould be a low probability of both failing to ii-iark real edge points nd a low probability of falsely arking non-edge points,

Good localization. Points ii-tarked as edge points should be close to te actual edge.

Only oe response per edge.

Canny defines a localization metric for a feature detector which is used in Sec-tion 44 for investigating the accuracy in locating the center of a light stripe.

The accuracy of dimensional measurements from visual 'images has been studied by groups at General Electric 128,155,156] and SRI International 88]. Mundy and Porter at G.E. determine the accuracy in measuring surfaces with reflectance variations. The technique has been applied to turbine blade inspection. Hill at SRI determines the accuracy of locating binary "blobs" in images based on the number of pxels illuminated by the blob. The accuracy of area calculations are also considered. A probabilistic approach was taken and results were verified with Monte Carlo simulations and laboratory experiments. A similar approach is used to determine the standard deviation in fitted line parameters in Section 43.

Using Multiple Measurements

The error in estimating variables from noisy measurements may be decreased by using multiple independent or partially dependent measurements. Additional mea-surements may come from the same sensor or a completely different source.

Bajcsy and Allen 89,15] integrate vision and touch to make measurements of points on the surfaces of objects. First, the outline of the object is determined by

• vision system. This information is then used to drive a manipulator fitted with

• touch sensor. A model of the object is constructed from the tactile data. Visual information is never directly integrated with tactile information so conflicting data from disparate sources is not dealt with.

Accumulation and propagation of errors 'in mechanical assemblies was studied by Taylor 189] and Brooks 341. Taylor propagates geometric errors through a physical model of an assembly. Brooks addresses a similar problem, but uses a

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W-1: Literature Review of Feature Extraction Techniques 107

symbolic rather than numerical representation. By assuming maximum bounds on the errors, Brooks is able to propagate certain geometric constraints to determine final errors from a number of sources. Both of these geometric error propagation systems assume a maximum error at each source (non-probabilistic) and will gve gross over estimates of errors if a significant number of sources- are involved.

Optimal estimation theory 641 may be applied to the best fit orientation and displacement estimation problem. The maximum likelihood estimator gives an estimate from overconstraining data weighted by te covariance between the com-ponents of the measurement. No prior knowledge about the position of the object being measured is assumed. A Kalman filter technique 64] may be used to op-timally update a current estimate from subsequent independent measurements.

Durrant-Whyte 55] combines information from independent observations to get a minimum-risk best estimate of the state of the environment. A Bayesian approach is used to combine errors and a non-recursive estimate is presented. Differential transformations as developed in 1471, are used to represent small errors in ori-entation and translation. The possibility of spurious measurements is taken into account and when it is likely that such a measurement occurred, it is rejected.

A significant number of measurements must be taken in order to do this reliably.

New estimates are propagated throug a world model to maintain consistency of the model.

Shekhar Khatib and Shimojo 1711 use a. non-probabilistic method to com-bine a number of rotation and translation measurements into a single estimate.

They use a quaternion representation for rotations and assume a diagonal weight-ing matrix for the set of measurements; thus, dependence between components of a measurement are ignored. Their results are similar to the maximum likelihood

re-sults from optimal estimation theory ith diagonal covariance matrices. Smith and Cheeseman 179,1801 develop two ways of combining wat they call "fuzzy transfor-mations." Compounding two fuzzy transformations increases the uncertainty and merging them decreases the uncertainty. Compounding uses the Jacobian of the resultant transformation (derivatives are ith respect to te components of the un-compounded transformations) and the covariance matrices of the unun-compounded transformations. Merging uses an extended Kalman filtering result. An example covariance matrix calculation for measurements of the planar position of a mobile robot is given.

Chapter 4 Feature Localization Uing a Light Stripe Vision System 108

Light Plane

CLI I L U CL

Figure 41: Three line segments generated by the intersection of a plane of light and the surfaces of a polyhedral feature may be sensed b a deo camera and used to locate a part.