Shape-based interpolation as applied to binary images causes the interpolation process to be influenced by the shape of the object. It accomplishes this by first applying a distance transform to the data. This results in the creation of a grey-level data set in which the value at each point represents the minimum distance from that point to the surface of the object. (By convention, points inside the object are assigned positive values; points outside are assigned negative values.) This distance transformed data set is then interpolated using linear or higher-order interpolation and is then thresholded at a distance value of zero to produce the interpolated binary data set. Here, the authors describe a new method that extends shape-based interpolation to grey-level input data sets. This generalization consists of first lifting the n-dimensional (n-D) image data to represent it as a surface, or equivalently as a binary image, in an (n+1)-dimensional [(n+1)-D] space. The binary shape-based method is then applied to this image to create an (n+1)-D binary interpolated image. Finally, this image is collapsed (inverse of lifting) to create the n-D interpolated grey-level data set. The authors have conducted several evaluation studies involving patient computed tomography (CT) and magnetic resonance (MR) data as well as mathematical phantoms. They all indicate that the new method produces more accurate results than commonly used grey-level linear interpolation methods, although at the cost of increased computation.

The purpose of this paper is to describe a framework for evaluating image segmentation algorithms. Image segmentation consists of object recognition and delineation. For evaluating segmentation methods, three factors -precision (reproducibility), accuracy (agreement with truth), and efficiency (time taken) -need to be considered for both recognition and delineation. To assess precision, we need to choose a figure of merit (FOM), repeat segmentation considering all sources of variation, and determine variations in FOM via statistical analysis. It is impossible usually to establish true segmentation. Hence, to assess accuracy, we need to choose a surrogate of true segmentation and proceed as for precision. To assess efficiency, both the computational and the user time required for algorithm and operator training and for algorithm execution should be measured and analyzed. Precision, accuracy, and efficiency are interdependent. It is difficult to improve one factor without affecting others. Segmentation methods must be compared based on all three factors. The weight given to each factor depends on application.

To aid in the display, manipulation, and analysis of biomedical image data, they usually need to he converted to data of isotropic discretization through the process of interpolation. Traditional techniques consist of direct interpolation of the grey values. When user interaction is called for in image segmentation, as a consequence of these interpolation methods, the user needs to segment a much greater (typically 4-10x) amount of data. To mitigate this problem, a method called shape-based interpolation of binary data was developed 121. Besides significantly reducing user time, this method has been shown to provide more accurate results than grey-level interpolation. We proposed an approach for the interpolation of grey data of arbitrary dimensionality that generalized the shape-based method from binary to grey data. This method has characteristics similar to those of the binary shape-based method. In particular, we showed preliminary evidence that it produced more accurate results than conventional grey-level interpolation methods. In this paper, concentrating on the three-dimensional (3-D) interpolation problem, we compare statistically the accuracy of eight different methods: nearest-neighbor, linear grey-level, grey-level cubic spline, grey-level modified cubic spline, Goshtasby et al., and three methods from the grey-level shape-based class. A population of patient magnetic resonance and computed tomography images, corresponding to different parts of the human anatomy, coming from different three-dimensional imaging applications, are utilized for comparison. Each slice in these data sets is estimated by each interpolation method and compared to the original slice at the same location using three measures: mean-squared difference, number of sites of disagreement, and largest difference. The methods are statistically compared pairwise based on these measures. The shape-based methods statistically significantly outperformed all other methods in all measures in all applications considered here with a statistical relevance ranging from 10% to 32% (mean = 15%) for mean-squared difference.

The Medical Image Processing Group at the University of Pennsylvania has been developing (and distributing with source code) medical image analysis and visualization software systems for a long period of time. Our most recent system, 3DVIEWNIX, was first released in 1993. Since that time, a number of significant advancements have taken place with regard to computer platforms and operating systems, networking capability, the rise of parallel processing standards, and the development of open-source toolkits. The development of CAVASS by our group is the next generation of 3DVIEWNIX. CAVASS will be freely available and open source, and it is integrated with toolkits such as Insight Toolkit and Visualization Toolkit. CAVASS runs on Windows, Unix, Linux, and Mac but shares a single code base. Rather than requiring expensive multiprocessor systems, it seamlessly provides for parallel processing via inexpensive clusters of work stations for more time-consuming algorithms. Most importantly, CAVASS is directed at the visualization, processing, and analysis of 3-dimensional and higher-dimensional medical imagery, so support for digital imaging and communication in medicine data and the efficient implementation of algorithms is given paramount importance.