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“A Joint Detection-Estimation Approach to Boundary Estimation”
by Simon Lopez-Mora
June 1977
The estimation of object boundaries based on noisy observations is considered in the context of joint detection and estimation.
The images are expressed as replacement processes and the boundaries modeled in terms of geometrical parameters associated with the object. The images studied have two textures, object and background, characterized by their first and second order statistics. A boundary processor consisting of optima estimator and detector is derived, for an appropriately chosen cost function. Differences between the cost function and resultant processor with other costs and estimator-detector pairs used previously in other applications is indicated. The optimal solution involves a nonlinear estimator and a detector with a variable threshold dependent on the estimator output.
Further, because of information restrictions imposed on the estimator that alleviate its computational requirements, a recursive, easily implementable algorithm, updating only the first two moments is derived, and subsequently used to evaluate the estimate as well as to perform detection.
Experimental results are illustrated. Of particular significance is the applicability of said processor under very low signal to noise ratio conditions.