This paper presents a registration framework based on the polynomial expansion transform. The idea of polynomial expansion is that the image is locally approximated by polynomials at each pixel. Starting with observations of how the coefficients of ideal linear and quadratic polynomials change under translation and affine transformation, algorithms are developed to estimate translation and compute affine and deformable registration between a fixed and a moving image, from the polynomial expansion coefficients. All algorithms can be used for signals of any dimensionality. The algorithms are evaluated on medical data.

This paper presents a novel active surface segmentation algorithm using a multiscale shape representation and prior. We define a parametric model of a surface using spherical wavelet functions and learn a prior probability distribution over the wavelet coefficients to model shape variations at different scales and spatial locations in a training set. Based on this representation, we derive a parametric active surface evolution using the multiscale prior coefficients as parameters for our optimization procedure to naturally include the prior in the segmentation framework. Additionally, the optimization method can be applied in a coarse-to-fine manner. We apply our algorithm to the segmentation of brain caudate nucleus, of interest in the study of schizophrenia. Our validation shows our algorithm is computationally efficient and outperforms the Active Shape Model algorithm by capturing finer shape details.

The accuracy and precision of segmentations of medical images has been difficult to quantify in the absence of a "ground truth" or reference standard segmentation for clinical data. Although physical or digital phantoms can help by providing a reference standard, they do not allow the reproduction of the full range of imaging and anatomical characteristics observed in clinical data. An alternative assessment approach is to compare to segmentations generated by domain experts. Segmentations may be generated by raters who are trained experts or by automated image analysis algorithms. Typically these segmentations differ due to intra-rater and inter-rater variability. The most appropriate way to compare such segmentations has been unclear. We present here a new algorithm to enable the estimation of performance characteristics, and a true labeling, from observations of segmentations of imaging data where segmentation labels may be ordered or continuous measures. This approach may be used with, amongst others, surface, distance transform or level set representations of segmentations, and can be used to assess whether or not a rater consistently over-estimates or under-estimates the position of a boundary.

The concept of the Logarithm of the Odds (LogOdds) is frequently used in areas such as artificial neural networks, economics, and biology. Here, we utilize LogOdds for a shape representation that demonstrates desirable properties for medical imaging. For example, the representation encodes the shape of an anatomical structure as well as the variations within that structure. These variations are embedded in a vector space that relates to a probabilistic model. We apply our representation to a voxel based segmentation algorithm. We do so by embedding the manifold of Signed Distance Maps (SDM) into the linear space of LogOdds. The LogOdds variant is superior to the SDM model in an experiment segmenting 20 subjects into subcortical structures. We also use LogOdds in the non-convex interpolation between space conditioned distributions. We apply this model to a longitudinal schizophrenia study using quadratic splines. The resulting time-continuous simulation of the schizophrenic aging process has a higher accuracy then a model based on convex interpolation.

Recent work shows that diffusion tensor imaging (DTI) can help resolving thalamic nuclei based on the characteristic fiber orientation of the corticothalamic/thalamocortical striations within each nucleus. In this paper we describe a novel segmentation method based on spectral clustering. We use Markovian relaxation to handle spatial information in a natural way, and we explicitly minimize the normalized cut criteria of the spectral clustering for a better optimization. Using this modified spectral clustering algorithm, we can resolve the organization of the thalamic nuclei into groups and subgroups solely based on the voxel affinity matrix, avoiding the need for explicitly defined cluster centers. The identification of nuclear subdivisions can facilitate localization of functional activation and pathology to individual nuclear subgroups.