Centered pyramids

Abstract

Abstract-Quadtree-like pyramids have the advantage of resulting in a multiresolution representation where each pyramid node has four unambiguous parents. Such a centered topology guarantees a clearly defined up-projection of labels. This concept has been successfully and extensively used in applications of contour detection, object recognition and segmentation. Unfortunately, the quadtree-like type of pyramid has poor approximation powers because of the employed piecewise-constant image model. This paper deals with the construction of improved centered image pyramids in terms of general approximation functions. The advantages of the centered topology such a symmetry, consistent boundary conditions and accurate up-projection of labels are combined with a more faithful image representation at coarser pyramid levels. We start by introducing a general framework for the design of least squares pyramids using the standard filtering and decimation tools. We give the most general explicit formulas for the computation of the filter coefficients by any (well behaving) approximation function in both the continuous (L2) and the discrete (l2) norm. We then define centered pyramids and provide the filter coefficients for odd spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications.

Investigation and evaluation of optimal registration for medical CT images

“…B-spline registration manipulates the mesh via a set of control points and naturally lends itself for multiresolution registration [9][10][11][12] . In this paper, the registration pyramids consisting of multiple resolution levels were constructed by setting different levels of B-spline control points, and then registration was performed via a "coarse-to-fine" registration strategy (Figure 2).…”

Data Registration and Fusion

“…Systematic research into B-spline-based hierarchical registration has been carried out by [15,20,91,94,95]. In these splinebased registration methods, pyramids were constructed by preWltering and then downsampling the images.…”

Directional Coherence Interpolation for Three-Dimensional Gray-Level Images

“…During iterations, for each cube, the MCD is updated by evaluating the objective function in Eq. (2). The final converged coherence map gives us a set of smoothed MCDs for the corresponding cubes between the two image slices.…”