Flexible Alignment of Images Using B-Spline Reparameterization Based on Multi-resolution Representations - Computational Methods

We present a new flexible alignment method to align two or more similar images, especially biological images. By minimizing an energy functional measuring the difference of the initial image and target image, an L
²
-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in the temporal direction. Multi-resolution representations are used for achieving efficient multi-scale alignment. The experimental results on 2D images show that the proposed method is efficient, effective, robust and capable of capturing the variation of the initial and target images, from large to small scale.