The purpose of this work is to compare the speed of isosurface rendering in software with that using dedicated hardware. Input data consist of 10 different objects from various parts of the body and various modalities (CT, MR, and MRA) with a variety of surface sizes (up to 1 million voxels/2 million triangles) and shapes. The software rendering technique consists of a particular method of voxel-based surface rendering, called shell rendering. The hardware method is OpenGL-based and uses the surfaces constructed from our implementation of the Marching Cubes algorithm. The hardware environment consists of a variety of platforms, including a Sun Ultra I with a Creator3D graphics card and a Silicon Graphics Reality Engine II, both with polygon rendering hardware, and a 300 MHz Pentium PC. The results indicate that the software method (shell rendering) was 18 to 31 times faster than any hardware rendering methods. This work demonstrates that a software implementation of a particular rendering algorithm (shell rendering) can outperform dedicated hardware. We conclude that, for medical surface visualization, expensive dedicated hardware engines are not required. More importantly, available software algorithms (shell rendering) on a 300 MHz Pentium PC outperform the speed of rendering via hardware engines by a factor of 18 to 31.

Image interpolation is an important operation that is widely used in medical imaging, image processing, and computer graphics. A variety of interpolation methods are available in the literature. However, their systematic evaluation is lacking. In a previous paper, we presented a framework for the task-independent comparison of interpolation methods based on certain image-derived figures of merit using a variety of medical image data pertaining to different parts of the human body taken from different modalities. In this work, we present an objective task-specific framework for evaluating interpolation techniques. The task considered is how the interpolation methods influence the accuracy of quantification of the total volume of lesions in the brain of multiple sclerosis (MS) patients. Sixty lesion-detection experiments coming from ten patient studies, two subsampling techniques and the original data, and three interpolation methods are carried out, along with a statistical analysis of the results.

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.

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.