The scattered field from an object, when illuminated with ultrasound, is useful in the reconstruction of it's cross section - a problem broadly classified as 'tomography'. In many situations of medical imaging, we will be interested in getting to know the location and the extent of growth of the inhomogeneity. The Maximum Likelihood (ML) estimation of the location and the shape parameters (of scale and orientation angle), has been done along with the corresponding CR bounds, for the case of weakly scattering objects, where the Fourier Diffraction Theorem(FDT) holds. It has been found that the a-priori information of a reference object function helps in drastic reduction of the number of receivers and illuminations required. For a polygonal object, the shape is specified, when the corner locations are known. We have formulated the problem as, estimation of the frequencies of sum of undamped sinusoids. The result is a substantial reduction in the number of illuminations and receivers required. For acoustically soft and rigid polygons, where the FDT does not hold, the necessary theory is developed to show the dependence of the scattered field on the corner location, using an On Surface Radiation Condition(OSRC). The corner locations are estimated along similar lines, to the one adopted for the weakly scattering objects.