Surface Estimation via Analysis Method: A Constrained Inverse Problem Approach

Ultrasonic imaging is a common technique in nondestructive evaluation, as it presents advantages such as low cost and safety of operation. In many industries, the interior inspection of objects with complex geometry has become a necessity. This kind of inspection requires the transducer to be coupled to the object with the use of some technique, such as immersing the object in water. When doing so, the geometry of the object surface must be known a priori or estimated. Recent methods for surface estimation start with an image of the interface between water and the specimen. Then, the surface is estimated by processing the image using different strategies. In this article, the strategy to extract the surface profile is based on an analysis-based inverse problem, hence named surface estimation via analysis method (SEAM). The problem formulation aims to reduce the noise in the estimate and also, by including priors, reach more accurate estimates. By using a second-order total variation regularization, which favors piecewise linear functions, the proposed method can describe a great range of surface profiles. Experiments were performed to evaluate the proposed method on surface profile estimation and results show good agreement with references and lower errors than methods in the literature. In addition, the estimated profiles enhance the imaging of the interior of objects, allowing better visualization of internal defects.