On the Cost of Approximating and Recogni?ing a Noise Perturbed Straicht Line or a Ouadfatic Curve Segment in the Plane

Approximation of noisy data in the plane by straight lines or elliptic: or single-branch hyperbolic curve segments arises in pattern recogniticn, data compaction, and other problems. A number of questions concerning the efficient search fo_ and approximation of data by such curves are examined. Fecursive least-squares linear curve-fitting is used, and ellipses and hyperbolas are parameterized as quadratic functions in x and v. The error minimized by the algorithm is interpreted. cpu times for estimating parameters for fitting stra^.ith' lines and quadratic curves are determined and compared. cpu time for data search is also determined for Oie case of straight line fitting. Quadratic curve f -tine is shown to require about six tines as much cpu time as does straight line fitting. Curves relating cpu time and fitting error arc °etermined for straight line fitting. Lastly, results are derived cn early sequential determination of whether or not the underlying curve is a straight line. (NASA 142 906) ON THE COST Oi APP?0X1 Y ATIvr, AND P rCCGNIZING A NOISY.? N75-27bu2 PFCTU?BLD STFAI(,Hr LINE U p A :QUAD'AT,^ CUFy SFGMENT IN THr PLAN (thrown Univ.) •,9 p NC Unclas $3.75 G 3/n 3 2.15