We propose a new measure, the method noise, to evaluate and compare the performance of digital image denoising methods. We first compute and analyze this method noise for a wide class of denoising algorithms, namely the local smoothing filters. Second, we propose a new algorithm, the nonlocal means (NL-means), based on a nonlocal averaging of all pixels in the image. Finally, we present some experiments comparing the NL-means algorithm and the local smoothing filters.

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A non-local algorithm for image denoising

The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics In spite of the sophistication of the recently proposed methods, m

/pdf/a-review-of-image-denoising-algorithms-with-a-new-one-4vfxkcsntt.pdf

A Review of Image Denoising Algorithms, with a New One

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

A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in two dimensions and shows that if the local ' mesh Reynolds number ', based on the size of the mesh used in the solution, exceeds a certain fixed value, the numerical solution will not converge.

On the Navier-Stokes equations

A simplified color image formation model is used to construct an algorithm for image reconstruction from CCD sensors samples. The proposed method involves two successive steps. The first is motivated by Cok's (1994) template matching technique, while the second step uses steerable inverse diffusion in color. Classical linear signal processing techniques tend to oversmooth the image and result in noticeable color artifacts along edges and sharp features. The question is how should the different color channels support each other to form the best possible reconstruction. Our answer is to let the edges support the color information, and the color channels support the edges, and thereby achieve better perceptual results than those that are bounded by the sampling theoretical limit.

/pdf/demosaicing-image-reconstruction-from-color-ccd-samples-2gs8ggnklv.pdf

Demosaicing: image reconstruction from color CCD samples

On Gabor's contribution to image enhancement

The modulation transfer function (MTF) is a fundamental tool for assessing the performance of imaging systems.
It has been applied to a range of capture and output devices, including printers and even the media itself. In this
paper, we consider the problem of measuring the MTF of image capture devices. We analyze the factors that
limit the MTF of a capture device. Then, we examine three different approaches to this task based, respectively,
on a slant-edge target, a sinewave target, and a grill pattern. We review the mathematical relationship between
the three different methods, and discuss their comparative advantages and disadvantages. Finally, we present
experimental results for MTF measurement with a number of different commercially available image capture devices
that are specifically designed for capture of 2D reflection or transmission copy. These include camera-based
systems, flat-bed scanners, and a drum scanner.

Measuring the modulation transfer function of image capture devices: what do the numbers really mean?

A neural network (112) is trained and used to reduce artifacts in spatial domain representations of images that ere compressed by transformed method and then decompressed. For example, the neural network can (112) be trained and used to reduce artifacts such as blocking and ringing artifacts in JPEG images.

Image artifact reduction using a neural network

Systems and methods of face and skin sensitive image enhancement are disclosed. In one aspect, a face map (60) that includes for each pixel of an input image (24) a respective face probability value indicating a degree to which the pixel corresponds to a human face is calculated. A skin map (62) that includes for each pixel of the input image (24) a respective skin probability value indicating a degree to which the pixel corresponds to human skin is ascertained. The input image (24) is enhanced with an enhancement level that varies pixel-by-pixel in accordance with the respective face probability values and the respective skin probability values. In another aspect, a facial content measurement value indicating a degree to which an input image (24) contains human face content is ascertained. A tone-correction process is tuned in accordance with the facial content measurement value. The input image (24) is enhanced in accordance with the tuned tone-correction process.

Face and skin sensitive image enhancement

Interactive detection of system anomalies is disclosed. One example is a system including a data processor, an anomaly processor, and an interaction processor. Input data related to a series of events and telemetry measurements is received by the data processor. The anomaly processor detects presence of a system anomaly in the input data, the system anomaly indicative of a rare situation that is distant from a norm of a distribution based on the series of events and telemetry measurements. The interaction processor is communicatively linked to the anomaly processor and to an interactive graphical user interface. The interaction processor displays, via the interactive graphical user interface, an output data stream based on the presence of the system anomaly, receives, from the interactive graphical user interface, feedback data associated with the output data stream, and provides the feedback data to the anomaly processor for operations analytics based on the feedback data.

Mani Fischer

Papers

On Gabor's contribution to image enhancement

Measuring the modulation transfer function of image capture devices: what do the numbers really mean?

Image artifact reduction using a neural network

Face and skin sensitive image enhancement

Interactive detection of system anomalies