A Fast Registration Method Using IP and Its Application to Ultrasound Image Registration

Abstract

This paper presents a fast registration method based on solving an energy minimization problem derived by implicit polynomials (IPs). Once a target object is encoded by an IP, it will be driven fast towards a corresponding source object along the IP's gradient flow without using point-wise correspondences. This registration process is accelerated by a new IP transformation method. Instead of the time-consuming transformation to a large discrete data set, the new method can transform the polynomial coefficients to maintain the same Euclidean transformation. Its computational efficiency enables us to improve a new application for real-time Ultrasound (US) pose estimation. The reported experimental results demonstrate the capabilities of our method in overcoming the limitations of a noisy, unconstrained, and freehand US image, resulting in fast and robust registration.

The Richer Representation the Better Registration

“…In addition to the qualitative evaluation presented with 2D contours 3D real objects have been registered with the proposed approach and compared with four techniques (i.e., [13], [15]- [17]) from the state of the art, together with the classical ICP [7]. Each technique iterates until one of these stopping criteria is reaches: if the number of iterations exceeds a maximum bound (#Iter = 40) or the relative registration error is smaller than the given threshold ( < 0.005); relative registration error is defined as: = |E t − E t −1 |/E t , where E t refers to the registration error between the target and source set at iteration t.…”

“…Unfortunately, computing the principal curvatures over the point cloud is computationally expensive and sensitive to noise. Finally, [17] proposes a distance field approximation by using an implicit polynomial [22]. This IP is considered to define a gradient flow that drives the source towards the target without using pointwise correspondences.…”

“…In this work we use LMA for the optimization part [26], which is particularly proposed for non-linear least squares forms as the case in (17). This method proposes a tradeoff between the gradient descent and the Gauss−Newton algorithm.…”

“…In order to handle LMA, the value of each residual in (17) and its partial derivatives, which are expressed in a Jacobian matrix J , must be provided. Since LMA uses the gradient information and the first order distance approximation in (17) captures this information, higher degree approximations would not benefit the result of LMA. It should be mentioned that the derivatives of summands in (17) must be calculated with respect to the parameters in .…”

“…[12]- [14]). In [15]- [17] the point-wise problem is avoided by using either the distance field of the target set or the distance fields of both target and source sets. More details about all these approaches are given in the next section.…”