Kernel Target Alignment

This paper proposes a new Tensorial Representation of HSI color images, where each pixel is a 2 × 2 second order tensor, that can be represented by an ellipse. A proposed tensorial morphological gradient (TMG) is defined as the maximum dissimilarity over the neighborhood determined by a structuring element, and is used in the watershed segmentation framework. Many tensor dissimilarity functions are tested and other color gradients are compared. The comparison uses a new methodology for qualitative evaluation of color image segmentation by watershed, where the watershed lines of the n most significant regions are overlaid on the original image for visual comparison. Experiments show that the TMG using Frobenius norm dissimilarity function presents superior segmentation results, in comparison to other tested gradients.

The sensitivity of parameters in computational science problems is difficult to assess, especially for algorithms with multiple input parameters and diverse outputs. This work seeks to explore sensitivity analysis in the visualization domain, introducing novel techniques for respective visual analyses of parameter sensitivity in multi-dimensional algorithms. First, the sensitivity analysis background is revisited, highlighting the definition of sensitivity analysis and approaches analyzing global and local sensitivity as well as the differences of sensitivity analysis to the more common uncertainty analysis. We introduce and explore parameter sensitivity using visualization techniques from overviews to details on demand, covering the analysis of all aspects of sensitivity in a prototypical implementation. The respective visualization techniques outline the algorithmic in-and outputs including indications, on how sensitive an input is with regard to the outputs. The detailed sensitivity information is communicated through constellation plots for the exploration of input and output spaces. A matrix view is discussed for localized information on the sensitivity of specific outputs to specific inputs. A 3D view provides the link of the parameter sensitivity to the spatial domain, in which the results of the multi-dimensional algorithms are embedded. The proposed sensitivity analysis techniques are implemented and evaluated in a prototype called Sensitivity Explorer. We show that Sensitivity Explorer reliably identifies the most influential parameters and provides insights into which of the output characteristics these affect as well as to which extent.

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In segmentation techniques for Diffusion Tensor Imaging (DTI) data, the similarity of diffusion tensors must be assessed for partitioning data into regions which are homogeneous in terms of tensor characteristics. Various distance measures have been proposed in literature for analysing the similarity of diffusion tensors (DTs), but selecting a measure suitable for the task at hand is difficult and often done by trialand- error. We propose a novel approach to semiautomatically define the similarity measure or combination of measures that better suit the data. We use a linear combination of known distance measures, jointly capturing multiple aspects of tensor characteristics, for comparing DTs with the purpose of image segmentation. The parameters of our adaptive distance measure are tuned for each individual segmentation task on the basis of user-selected ROIs using the concept of Kernel Target Alignment. Experimental results support the validity of the proposed method.

Anna Vilanova is an assistant professor and head of a research group in the Biomedical Image Analysis unit of the Biomedical Engineering department at the Eindhoven University of Technology. She received her PhD degree in 2001 from the Vienna University of Technology. Her current research interests are focused on medical visualization and image analysis.

In segmentation techniques for Diffusion Tensor Imaging (DTI) data, the similarity of diffusion tensors must be assessed for partitioning data into regions which are homogeneous in terms of tensor characteristics. Various distance measures have been proposed in literature for analysing the similarity of diffusion tensors (DTs), but selecting a measure suitable for the task at hand is difficult and often done by trialand-error.

This paper presents a segmentation technique for diffusion tensor imaging (DTI). This technique is based on a tensorial morphological gradient (TMG), defined as the maximum dissimilarity over the neighborhood. Once this gradient is computed, the tensorial segmentation problem becomes an scalar one, which can be solved by conventional techniques, such as watershed transform and thresholding. Similarity functions, namely the dot product, the tensorial dot product, the J-divergence and the Frobenius norm, were compared, in order to understand their differences regarding the measurement of tensor dissimilarities. The study showed that the dot product and the tensorial dot product turned out to be inappropriate for computation of the TMG, while the Frobenius norm and the J-divergence were both capable of measuring tensor dissimilarities, despite the distortion of Frobenius norm, since it is not an affine invariant measure. In order to validate the TMG as a solution for DTI segmentation, its computation was performed using distinct similarity measures and structuring elements. TMG results were also compared to fractional anisotropy. Finally, synthetic and real DTI were used in the method validation. Experiments showed that the TMG enables the segmentation of DTI by watershed transform or by a simple choice of a threshold. The strength of the proposed segmentation method is its simplicity and robustness, consequences of TMG computation. It enables the use, not only of well-known algorithms and tools from the mathematical morphology, but also of any other segmentation method to segment DTI, since TMG computation transforms tensorial images in scalar ones.

In segmentation techniques for Diffusion Tensor Imaging (DTI) data, the similarity of diffusion tensors must be assessed for partitioning data into regions which are homogeneous in terms of tensor characteristics. Various distance measures have been proposed in literature for analysing the similarity of diffusion tensors (DTs), but selecting a measure suitable for the task at hand is difficult and often done by trialand- error. We propose a novel approach to semiautomatically define the similarity measure or combination of measures that better suit the data. We use a linear combination of known distance measures, jointly capturing multiple aspects of tensor characteristics, for comparing DTs with the purpose of image segmentation. The parameters of our adaptive distance measure are tuned for each individual segmentation task on the basis of user-selected ROIs using the concept of Kernel Target Alignment. Experimental results support the validity of the proposed method.