Periodic quasi-orthogonal spline bases and applications to least-squares curve fitting of digital images

Image registration by "super-curves"

We solve the 2-D affine image registration problem by curve matching and alignment. Our approach starts with a super-curve, which is formed by superimposing two affine related curves in one coordinate system. We use B-spline fusion technique to find a single B-spline approximation of the super-curve and a registration between the two curves simultaneously. This approach achieves superior accuracy and efficiency in curve matching and alignment. We then address the occlusion problem by finding partial match between the curves segmented using inflections and cusps, which are affine invariant. The combination of edge detection and curve alignment lead to accurate image registration.

Fast and accurate edge-based segmentation with no contour smoothing in 2-D real images

In this paper we propose an edge-based segmentation algorithm built on a new type of active contour which is fast, has a low computational complexity and does not introduce unwanted smoothing on the retrieved contours. The contours are always returned as closed chains of points, resulting in a very useful base for subsequent shape representation techniques.

Unsupervised contour representation and estimation using B-splines and a minimum description length criterion

This paper describes a new approach to adaptive estimation of parametric deformable contours based on B-spline representations. The problem is formulated in a statistical framework with the likelihood function being derived from a region-based image model. The parameters of the image model, the contour parameters, and the B-spline parameterization order (i.e., the number of control points) are all considered unknown. The parameterization order is estimated via a minimum description length (MDL) type criterion. A deterministic iterative algorithm is developed to implement the derived contour estimation criterion, the result is an unsupervised parametric deformable contour: it adapts its degree of smoothness/complexity (number of control points) and it also estimates the observation (image) model parameters. The experiments reported in the paper, performed on synthetic and real (medical) images, confirm the adequate and good performance of the approach.