We call methods for achieving high-resolution enlargements of pixel-based images super-resolution algorithms. Many applications in graphics or image processing could benefit from such resolution independence, including image-based rendering (IBR), texture mapping, enlarging consumer photographs, and converting NTSC video content to high-definition television. We built on another training-based super-resolution algorithm and developed a faster and simpler algorithm for one-pass super-resolution. Our algorithm requires only a nearest-neighbor search in the training set for a vector derived from each patch of local image data. This one-pass super-resolution algorithm is a step toward achieving resolution independence in image-based representations. We don't expect perfect resolution independence-even the polygon representation doesn't have that-but increasing the resolution independence of pixel-based representations is an important task for IBR.

/pdf/example-based-super-resolution-3nf17iliy7.pdf

Example-based super-resolution

Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation kernels of finite size have been introduced. This paper compares 1) truncated and windowed sine; 2) nearest neighbor; 3) linear; 4) quadratic; 5) cubic B-spline; 6) cubic; g) Lagrange; and 7) Gaussian interpolation and approximation techniques with kernel sizes from 1/spl times/1 up to 8/spl times/8. The comparison is done by: 1) spatial and Fourier analyses; 2) computational complexity as well as runtime evaluations; and 3) qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing. For local and Fourier analyses, a standardized notation is introduced and fundamental properties of interpolators are derived. Successful methods should be direct current (DC)-constant and interpolators rather than DC-inconstant or approximators. Each method's parameters are tuned with respect to those properties. This results in three novel kernels, which are introduced in this paper and proven to be within the best choices for medical image interpolation: the 6/spl times/6 Blackman-Harris windowed sinc interpolator, and the C2-continuous cubic kernels with N=6 and N=8 supporting points. For quantitative error evaluations, a set of 50 direct digital X-rays was used. They have been selected arbitrarily from clinical routine. In general, large kernel sizes were found to be superior to small interpolation masks. Except for truncated sine interpolators, all kernels with N=6 or larger sizes perform significantly better than N=2 or N=3 point methods (p/spl Lt/0.005). However, the differences within the group of large-sized kernels were not significant. Summarizing the results, the cubic 6/spl times/6 interpolator with continuous second derivatives, as defined in (24), can be recommended for most common interpolation tasks. It appears to be the fastest six-point kernel to implement computationally. It provides eminent local and Fourier properties, is easy to implement, and has only small errors. The same characteristics apply to B-spline interpolation, but the 6/spl times/6 cubic avoids the intrinsic border effects produced by the B-spline technique. However, the goal of this study was not to determine an overall best method, but to present a comprehensive catalogue of methods in a uniform terminology, to define general properties and requirements of local techniques, and to enable the reader to select that method which is optimal for his specific application in medical imaging.

/pdf/survey-interpolation-methods-in-medical-image-processing-erlouqboei.pdf

Survey: interpolation methods in medical image processing

This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into historical perspective. A summary of the insights and recommendations that follow from relatively recent theoretical as well as experimental studies concludes the presentation.

/pdf/prolog-to-a-chronology-of-interpolation-from-ancient-3h41hasu4i.pdf

Prolog to a chronology of interpolation: from ancient astronomy to modern signal and image processing

A technique for enhancing the perceptual sharpness of an image is described. The enhancement algorithm augments the frequency content of the image using shape-invariant properties of edges across scale by using a nonlinearity that generates phase coherent higher harmonics. The procedure utilizes the Laplacian transform and the Laplacian pyramid image representation. Results are presented depicting the power-spectra augmentation and the visual enhancement of several images. Simplicity of computations and ease of implementation allow for real-time applications such as high-definition television (HDTV).

/pdf/image-enhancement-by-nonlinear-extrapolation-in-frequency-4cek4btt5l.pdf

Image enhancement by nonlinear extrapolation in frequency space

In the unsharp masking approach for image enhancement,
a fraction of the highpass filtered version of the image is added to the original image to form the enhanced version The method is simple, but it suffers from two serious drawbacks First, it enhances the contrast in the darker areas perceptually much more strongly than that in the lighter areas Second, it enhances the noise and/or digitization effects, particularly in the darker regions, resulting in visually less pleasing enhanced images In general, noise can be suppressed with lowpass filters, which are associated with the blurring of the edges On the other hand, contrast can be enhanced with highpass filters, which are associated with noise amplification A reasonable solution, therefore, is to use suitable nonlinear filters which combine the features of both highpass and lowpass filters This paper outlines several new methods of unsharp masking based on the use of such nonlinear filters Computer simulations have verified the superior results obtained using these filters In addition, a new measure of contrast enhancement is introduced which quantitatively supports the improvement obtained using the proposed methods

Nonlinear unsharp masking methods for image contrast enhancement

A new adaptive algorithm for image interpolation with percep- tual edge enhancement is proposed. Here, perceptual means that edges are enhanced and interpolated in a visually pleasing way. Each pixel neighborhood is classified into one of three categories (constant, ori- ented, or irregular). In each case, an optimal interpolation technique finds the missing pixels without generating unpleasant artifacts such as aliasing or ringing effects. Furthermore, a quadratic Volterra filter is em- ployed to extract perceptually important details from the original image, which are then used to improve the overall sharpness and contrast. Both qualitative and quantitative simulation results clearly show the superiority of our method over standard low-pass interpolation algorithms such as bilinear, diamond-filter, or B-spline interpolation. © 1996 Society of Photo-Optical Instrumentation Engineers. Subject terms: image interpolation; zooming; quadratic Volterra filters; detail en- hancement; image enhancement; edge enhancement.

Edge-enhanced image zooming

An inherent problem in most image enhancement schemes is the amplification of noise, which, due to Weber's law, is mostly visible in the darker portions of an image. Using a special class of quadratic Volterra filters, we can adapt the enhancement process in a computationally efficient way to the local image brightness because these filters are approximately equivalent to the product of a local mean estimator and a highpass filter. We analyze and derive this subclass of quadratic Volterra filters by investigating the 1-D case first, and then we generalize the results to two dimensions. An important property of these filters is that they map sinusoidal inputs to constant outputs, which allows us to develop a new filter characterization that is more intuitive for our application than the 4-D frequency response. This description finally leads to a novel least-squares design methodology. Image enhancement results using our Volterra filters are superior to those obtained with standard linear filters, which we demonstrate both quantitatively and qualitatively.

A general framework for quadratic Volterra filters for edge enhancement

We propose a modification of the standard error-diffusion technique for image halftoning that enhances edges and textures by reducing the diffusion of the quantization error across edges. It employs a quadratic Volterra filter that extracts features from the original gray- scale image and adapts the feedback loop to the local characteristics of the image. The additional computational complexity is small because the filter only uses a 333 region of support. Experimental comparisons of various techniques show that our modified error diffusion algorithm pro- duces sharper results with improved contrast and detail resolution for both gray-scale and color images. © 1996 Society of Photo-Optical Instrumenta- tion Engineers.

Stefan Thurnhofer

Papers

Edge-enhanced image zooming

A general framework for quadratic Volterra filters for edge enhancement

Detail‐enhanced error diffusion