Wavelet and shearlet

A visual servoing scheme consists of a closed-loop control approach that uses visual information feedback to control the motion of a robotic system. Probably the most popular visual servoing method is image-based visual servoing (IBVS). This kind of method uses geometric visual features extracted from the image to design the control law. However, extracting, matching, and tracking geometric visual features over time significantly limits the versatility of visual servoing controllers in various industrial and medical applications, in particular for “low-structured” medical images, e.g. ultrasounds and optical coherence tomography modalities. To overcome the limits of conventional IBVS, one can consider novel visual servoing paradigms known as “direct” or “featureless” approaches. This paper deals with the development of a new generation of direct visual servoing methods in which the signal control inputs are the coefficients of a multiscale image representation. In particular, we consider the use of multiscale image representations that are based on discrete wavelet and shearlet transforms. Up to now, one of the main obstacles in the investigation of multiscale image representations for visual servoing schemes was the issue of obtaining an analytical formulation of the interaction matrix that links the variation of wavelet and shearlet coefficients to the spatial velocity of the camera and the robot. In this paper, we derive four direct visual servoing controllers: two that are based on subsampled respectively non-subsampled wavelet coefficients and two that are based on the coefficients of subsampled respectively non-subsampled discrete shearlet transforms. All proposed controllers were tested in both simulation and experimental scenarios (using a six-degree-of-freedom Cartesian robot in an eye-in-hand configuration). The objective of this paper is to provide an analysis of the respective strengths and weaknesses of wavelet- and shearlet-based visual servoing controllers