Registration with a small number of sparse measurements

This work introduces a method for performing robust registration given the geometric model of an object and a small number (less than 20) of sparse point and surface normal measurements of the object’s surface. Such a method is of critical importance in applications such as probing-based surgical registration, contact-based localization, manipulating objects devoid of visual features, etc. Our approach for sparse point and normal registration (SPNR) is iterative in nature. In each iteration, the current best pose estimate is perturbed to generate several candidate poses. Among the generated poses, one pose is selected as the best, by evaluating an inexpensive cost function. This pose is used as the initial condition to estimate the locally optimum registration. This process is repeated until the registration estimate converges within a tolerance bound. Two variants are developed: deterministic (dSPNR) and probabilistic (pSPNR). The dSPNR is faster than pSPNR in converging to the local optimum, but the pSPNR requires fewer parameters to be tuned. The pSPNR also provides pose-uncertainty information in addition to the registration estimate. Both approaches were evaluated in simulation using various standard datasets and then compared with results obtained using state-of-the-art methods. Upon comparison with other methods, both dSPNR and pSPNR were found to be robust to initial pose errors as well as noise in measurements. The effectiveness of the approaches are also demonstrated with robot experiments for the application of probing-based registration.