Frequency-based nonrigid motion analysis: application to four dimensional medical images

Abstract

Abstract-We present a method for nonrigid motion analysis in time sequences of volume images (4D data). In this method, nonrigid motion of the deforming object contour is dynamically approximated by a physically-based deformable surface. In order to reduce the number of parameters describing the deformation, we make use of a modal analysis which provides a spatial smoothing of the surface. The deformation spectrum, which outlines the main excited modes, can be efficiently used for deformation comparison. Fourier analysis on time signals of the main deformation spectrum components provides a ternporal smoothing of the data. Thus a complex nonrigid deformation is described by only a few parameters: the main excited modes and the main Fourier harmonics. Therefore, 4D data can be analyzed in a very concise manner. The power and robustness of the approach is illustrated by various results on medical data. We believe that our method has important applications in automatic diagnosis of heart diseases and in motion compression.

Space and Time Shape Constrained Deformable Surfaces for 4D Medical Image Segmentation

“…Our concept of 4D deformable surface models combines spatial and temporal constraints which di ers from most previous approaches 12, 16,4] that decouple them. Furthermore, in contrast to the strategy presented in 7], the motion estimation is not parameterized by a global time-space transformation.…”

“…Tracking the LV m o t i o n i n 2 D o r 3D image sequences has led to several research e orts 10, 9, 2]. Tracking 12,16] and motion analysis 4,7] based on deformable models in 4D images take i n to account time continuity and periodicity t o i m p r o ve their robustness.…”

A scheme of colour image retrieval from databases

“…We will de®ne a mechanism to represent the value of the modal range as a function of this mode, as follows:ũ i t f i . We will call this representation the modal spectrum (Nastar and Ayache, 1996). In summary, it describes which modes and what quantity of them need to be excited in order to deform a shape enough to make it appear like another.…”

“…We have chosen a model of shape deformation proposed in Nastar (Nastar and Ayache, 1996) to establish the deformation we would have to apply to an object in order to transform it into another one, and in this way to be able to measure the energy used as a measure of object similarity. This model gives us an analytical expression of the vibration modes of the nodes situated on a closed curve (we are interested in contours of closed forms).…”

“…There are many references related to the idea of describing objects with a mode of non-rigid deformation (Terzopoulos et al, 1988;Bookstein, 1989;Pentland and Sclaro , 1991;Jain and Vailaya, 1998). We use here the main ideas from the Nastar deformable model (Nastar and Ayache, 1996).…”