A New Variational Approach for 3d Shape Registration

Abstract

Shape-based approaches became very popular in medical imaging. The key issue in these methods is the shape representation and registration. This paper introduces a new method for the ¿ shape registration problem by matching vector distance functions. The vector distance function representation is more flexible than the conventional signed distance map since it enables us to better control the shapes registration process by using more general transformations. Based on this model, a variational frame work is proposed for the global and local registration of shapes which does not need any point correspondences. A gradient descent optimization is used and efficiently can handle both the rigid and the non-rigid operations together. The registration of real 3D human teeth models demonstrates the potential of the proposed approach. INTRODUCTIONShapes registration is an important complex problem in computer vision, computer graphics and medical imaging. It has been handled in different manners in many applications like shape-based segmentation, shape recognition, and tracking. The shapes registration problem is formulated such that a transformation that moves a point from a given shape to a target one according to some dissimilarity measure [1], needs to be estimated. The dissimilarity measure can be defined according either to the curve or in the entire region enclosed by the curve.In [2], a 3D shape-segmentation approach was proposed which included a shape registration process. A shape model was built from a set of training shapes using signed distance functions (the conventional representation). A level set function evolves minimizing the shape alignment energy and the intensity gray level. But using a simple global transformation with homogenous scales(× Ü × Ý × Þ ×) is not enough specially when gathering training shapes from different patients scans. The registration process fails when the target shape has inhomogeneous scales.Also different shapes registration approaches were proposed in the literature for example [3,4,5,6]. These approaches suffer from various problems. Scale variations and This research has been supported by the National Science Foundation (NSF) Grant IIS-0513974. local deformations can not be covered in many cases. Also their dependency on the initialization represents one of the hardships.In [7], the distance function is used to implicitly represent planar shapes. The images of distance functions are globally registered using the mutual information approach. Open structures are represented by using only the distance transform without any sign which can not distinguish between points on different sides of the shape contour.Vector distance functions (VDF's) are used in [8] to evolve smooth manifolds. This representation defines a vector that connects any point in the space to the nearest point on the curve or surface. This representation can deal with shapes of different dimensions.We proposed shape representation by vector components in a different manner in our shape-based segmentation...

Three-dimensional dental X-ray imaging by combination of panoramic and projection data

“…Tikhonov regularization is not the only possible solution methodology for the inverse problem considered here. For example, level set methods are another promising class of approaches, see [1,6,12,18,23,28,32].…”