http://library.utia.cas.cz/prace/20030125.pdf

Image registration methods: a survey

http://ee.sharif.edu/~miap/Files/A%20Survey%20of%20Medical%20Image%20Registration.pdf

A survey of medical image registration.

Preface Through many centuries physics has been one of the most fruitful sources of inspiration for mathematics. As a consequence, mathematics has become an economic language providing a few basic principles which allow to explain a large variety of physical phenomena. Many of them are described in terms of partial diierential equations (PDEs). In recent years, however, mathematics also has been stimulated by other novel elds such as image processing. Goals like image segmentation, multiscale image representation, or image restoration cause a lot of challenging mathematical questions. Nevertheless, these problems frequently have been tackled with a pool of heuristical recipes. Since the treatment of digital images requires very much computing power, these methods had to be fairly simple. With the tremendous advances in computer technology in the last decade, it has become possible to apply more sophisticated techniques such as PDE-based methods which have been inspired by physical processes. Among these techniques, parabolic PDEs have found a lot of attention for smoothing and restoration purposes, see e.g. 113]. To restore images these equations frequently arise from gradient descent methods applied to variational problems. Image smoothing by parabolic PDEs is closely related to the scale-space concept where one embeds the original image into a family of subsequently simpler , more global representations of it. This idea plays a fundamental role for extracting semantically important information. The pioneering work of Alvarez, Guichard, Lions and Morel 11] has demonstrated that all scale-spaces fulllling a few fairly natural axioms are governed by parabolic PDEs with the original image as initial condition. Within this framework, two classes can be justiied in a rigorous way as scale-spaces: the linear diiusion equation with constant dif-fusivity and nonlinear so-called morphological PDEs. All these methods satisfy a monotony axiom as smoothing requirement which states that, if one image is brighter than another, then this order is preserved during the entire scale-space evolution. An interesting class of parabolic equations which pursue both scale-space and restoration intentions is given by nonlinear diiusion lters. Methods of this type have been proposed for the rst time by Perona and Malik in 1987 190]. In v vi PREFACE order to smooth the image and to simultaneously enhance semantically important features such as edges, they apply a diiusion process whose diiusivity is steered by local image properties. These lters are diicult to analyse mathematically , as they may act locally like a backward diiusion process. …

/pdf/anisotropic-diffusion-in-image-processing-z13u09qvsm.pdf

Anisotropic diffusion in image processing

Several existing volume rendering algorithms operate by factoring the viewing transformation into a 3D shear parallel to the data slices, a projection to form an intermediate but distorted image, and a 2D warp to form an undistorted final image. We extend this class of algorithms in three ways. First, we describe a new object-order rendering algorithm based on the factorization that is significantly faster than published algorithms with minimal loss of image quality. Shear-warp factorizations have the property that rows of voxels in the volume are aligned with rows of pixels in the intermediate image. We use this fact to construct a scanline-based algorithm that traverses the volume and the intermediate image in synchrony, taking advantage of the spatial coherence present in both. We use spatial data structures based on run-length encoding for both the volume and the intermediate image. Our implementation running on an SGI Indigo workstation renders a 2563 voxel medical data set in one second. Our second extension is a shear-warp factorization for perspective viewing transformations, and we show how our rendering algorithm can support this extension. Third, we introduce a data structure for encoding spatial coherence in unclassified volumes (i.e. scalar fields with no precomputed opacity). When combined with our shear-warp rendering algorithm this data structure allows us to classify and render a 2563 voxel volume in three seconds. The method extends to support mixed volumes and geometry and is parallelizable.

/pdf/fast-volume-rendering-using-a-shear-warp-factorization-of-11o5tav1m5.pdf

Fast volume rendering using a shear-warp factorization of the viewing transformation

Nonlinear diffusion filtering in image processing is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a discrete nonlinear diffusion scale-space framework we present semi-implicit schemes which are stable for all time steps. These novel schemes use an additive operator splitting (AOS), which guarantees equal treatment of all coordinate axes. They can be implemented easily in arbitrary dimensions, have good rotational invariance and reveal a computational complexity and memory requirement which is linear in the number of pixels. Examples demonstrate that, under typical accuracy requirements, AOS schemes are at least ten times more efficient than the widely used explicit schemes.

/pdf/efficient-and-reliable-schemes-for-nonlinear-diffusion-4kfamil4rw.pdf

Efficient and reliable schemes for nonlinear diffusion filtering

Contrast limited adaptive histogram equalization

This paper introduces a novel approach for speeding up the ray casting process commonly used in volume visualization methods This new method, called Ray Acceleration by Distance Coding, RADC for short, uses a 3D distance transform to determine the minimum distance to the nearest interesting object; the implementation of a fast andaccurate distance transform is described in detail High distance values, typically found at off-center parts of thevolume, cause many sample points to be skipped, thus significantly reducing the number of samples to be evaluatedduring the ray casting step The minimum distance values that are encountered while traversing the volume can be used for the identification of rays that do not hit objects Our experiments indicate that the RADC method can reduce the number of sample points by a factor between 5 and 20 1 INTRODUCTION In spite of the rapidly increasing computational power of modern workstations, interactive rendering of volumetricdatasets still poses tremendous problems due to the sheer amount of data that must be processed Although parallelcomputer architectures as Pixel Planes 51

Acceleration of ray-casting using 3-D distance transforms

The reconstruction of images is an important operation in many applications. From sampling theory, it is well known that the sine-function is the ideal interpolation kernel which, however, cannot be used in practice. In order to be able to obtain an acceptable reconstruction, both in terms of computational speed and mathematical precision, it is required to design a kernel that is of finite extent and resembles the sinc-function as much as possible. In this paper, the applicability of the sine-approximating symmetrical piecewise nth-order polynomial kernels is investigated in satisfying these requirements. After the presentation of the general concept, kernels of first, third, fifth and seventh order are derived. An objective, quantitative evaluation of the reconstruction capabilities of these kernels is obtained by analyzing the spatial and spectral behavior using different measures, and by using them to translate, rotate, and magnify a number of real-life test images. From the experiments, it is concluded that while the improvement of cubic convolution over linear interpolation is significant, the use of higher order polynomials only yields marginal improvement.

/pdf/image-reconstruction-by-convolution-with-symmetrical-1w9oztj4hv.pdf

Image reconstruction by convolution with symmetrical piecewise nth-order polynomial kernels

In clinical practice, Digital Subtraction Angiography (DSA) is a powerful technique for the visualization of blood vessels in the human body. The diagnostic relevance of the images is often reduced by artifacts which arise from the misalignment of successive images in the sequence, due to patient motion. In order to improve the quality of the subtraction images, several registration techniques have been proposed. However, because of the required computation times, it has never led to algorithms that are fast enough so as to be acceptable for integration in clinical applications. In this paper, a new approach to the registration of digital angiographic images is proposed. It involves an edge-based selection of control points for which the displacement is computed by means of template matching, and from which the complete displacement vector field is constructed by means of interpolation. The final warping of the images according to the calculated displacement vector field is performed real-time by graphics hardware. Experimental results with several clinical data sets show that the proposed algorithm is both effective and very fast.

/pdf/image-registration-for-digital-subtraction-angiography-uwkpvcb108.pdf

Image Registration for Digital Subtraction Angiography

Computerized systems and methods provide occlusion culling for efficiently rendering a three dimensional image. The systems and methods calculate a set of occluder shields in a voxel dataset using a transparency value associated with each voxel of the dataset. Next, the occluder shields are applied to the dataset to identify regions of the voxel data that do not contribute to the final image. Finally, the voxel data set can be rendered, excluding regions that do not contribute to the final image.

Karel J. Zuiderveld

Papers

Contrast limited adaptive histogram equalization

Acceleration of ray-casting using 3-D distance transforms

Image reconstruction by convolution with symmetrical piecewise nth-order polynomial kernels

Image Registration for Digital Subtraction Angiography

Occlusion culling for object-order volume rendering