In this paper, an object boundary estimator, applicable to a class of noisy images, will be introduced. The images considered will contain an object of interest within the background where the statistics of the object, background, noise, and boundary are given. The procedures developed are recursive and readily implementable on a digital computer. A number of examples are considered to illustrate the performance of the estimator.

A new approach to design of a recursive image enhancer is introduced when the image is characterized statistically by its mean and correlation function. A vector linear dynamical model is derived to represent the statistics of the processor output when several lines of the picture are processed simultaneously. Based on the vector model, a Kalman filter is designed and utilized to recursively enhance the image. The vector processing results in a simpler and more accurate image enhancement algorithm in comparison with scalar processing. Two examples, one with very low signal-to-noise ratio, are used to illustrate the effectiveness of the procedure. Finally, the performance of the vector and scalar estimators is compared.

In classical estimation theory, the observation is always assumed to contain the signal to be estimated. In practice, certain observations, or sequences of observations, may contain noise alone, only the probability of occurrence of such cases being available to the estimator. An example is trajectory tracking where the signal is first detected and then the estimator is allowed to process it for tracking purposes. However, any detection decision is associated with a false-alarm probability, which is the probability that the detected signal contains only noise. Minimum mean-square estimators are derived for two different forms of this problem; 1) when it is possible that the observation at any sample time contains signal or is noise alone, independent of the situation at any other sample, and 2) when the entire sequence of observations contains signal or is only noise. The estimators derived are of recursive form. A simple example is given for illustration.