| Analyzing 3D anatomical structures plays an important role in modern biology and medical science. Despite the fast development of 3D medical imaging techniques such as MRI and CT, 2D imaging methods such as microscopy still excel in terms of spatial resolution and the anatomical details in fine tissue structures. This calls for an effective volumetric image reconstruction method to find theorrespondence among a sequence of 2D images and recover the 3D coherence that is lost in the sampling process. In this dissertation, we introduce a novel general framework for modeling volumetric image reconstruction with a rigorous and symmetric formulation. The formulation is robust to the noise and corrupted slices by using a greater range of adaptive weights in the regularization energy. The geometrical shape difference between sections is explicitly encoded via large deformation models which provide a mathematical method to quantitatively measure the shape change. Finally, a polyaffine image transformation model is presented which combines the power of deformation and the simplicity of the affine transformation. |
