AG 4   Info

AG Audience

English

45 Minutes

Saarbrücken

We present a novel approach, called squared distance minimization (SDM), to computing a B-spline curve to approximate the model shape defined by unorganized and noisy data points. The key idea is the use of a new fitting error term, called the squared distance (SD) error term, defined by a quadratic approximant of squared distances from data points to a fitting curve. Through iterative minimization of the SD error term, SDM makes a properly specified initial B-spline curve converge toward the model shape. Because the SD error term measures faithfully the geometric distance between a fitting curve and a model shape, SDM attains faster and more stable convergence than the commonly used point distance (PD) error term and tangent distance (TD) error term. To explain the superior performance of SDM, we show that SDM is a quasi-Newton method which employs a carefully chosen and geometrically motivated positive definite approximant to

the true Hessian of the objective function, while the method based on the TD error term uses Gauss-Newton iterations and the PD error based optimization is a variant of the steepest descent method. The extension of SDM to surface fitting will also be discussed.

Volker Blanz

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