A Variational Model for Image Artifact Correction Based on Wasserstein Distance

Validation of non-uniform illumination correction techniques in microscopic digital TB images using image sharpness measures

We investigated a novel fast non-uniform illumination correction method for bi-level images. The proposed method divides a bi-level image into sub-images and roughly estimates block-wise illumination by low pass filtered maximum values of sub-images. After that, we apply bilinear interpolation using the block-wise illumination to estimate non-uniform illumination, and compensate for the effect of non-uniform illumination using the estimated illumination. Since the proposed method is not based on computation intensive iterative optimization, the proposed method can be used effectively for applications that require fast correction of non-uniform illumination. In simulations, the proposed method showed more than 20 times faster speed than existing entropy minimization method. Moreover, in simulations and experiments, the restored images by the proposed method were more close to true images than images restored by conventional method.

Variational method is a useful mathematical tool in various areas of research, espe- cially in image processing. Recently, solving image processing problems on general manifolds using variational techniques has become an important research topic. In this paper, we solve several image processing problems on general Riemann surfaces using variational models defined on surfaces. We propose an explicit method to solve variational problems on general Riemann surfaces, using the conformal parameterization and covariant derivatives defined on the surface. To simplify the com- putation, the surface is firstly mapped conformally to the two dimensional rectangular domains, by computing the holomorphic 1-form on the surface. It is well known that the Jacobian of a conformal map is simply the scalar multiplication of the conformal factor. Therefore with the conformal para- meterization, the covariant derivatives on the parameter domain are similar to the usual Euclidean differential operators, except for the scalar multiplication. As a result, any variational problem on the surface can be formulated to a 2D problem with a simple formula and efficiently solved by well developed numerical scheme on the 2D domain. With the proposed method, we solve various image processing problems on surfaces using different variational models, which include image segmen- tation, surface denoising, surface inpainting, texture extraction and automatic landmark tracking. Experimental results show that our method can effectively solve variational problems and tackle image processing tasks on general Riemann surfaces.

Image pre-processing is highly significant in automated analysis of microscopy images. In this work, non-uniform illumination correction has been attempted using the surface fitting method (SFM), multiple regression method (MRM), and bidirectional empirical mode decomposition (BEMD) in digital microscopy images of tuberculosis (TB). The sputum smear positive and negative images recorded under a standard image acquisition protocol were subjected to illumination correction techniques and evaluated by error and statistical measures. Results show that SFM performs more efficiently than MRM or BEMD. The SFM produced sharp images of TB bacilli with better contrast. To further validate the results, multifractal analysis was performed that showed distinct variation before and after implementation of illumination correction by SFM. Results demonstrate that after illumination correction, there is a 26% increase in the number of bacilli, which aids in classification of the TB images into positive and negative, as TB positivity depends on the count of bacilli.

Illumination uniformity is essential for quantitative analysis in fluorescence microscopy. However, fewer images or sparse intensity information can compromise correction quality of retrospective methods, whereas traditional prospective methods necessitate recalibration whenever imaging conditions change. In this paper, we theoretically for the first time analyze the impact of non-uniform illumination on quantitative fluorescence resonance energy transfer (FRET), which is also demonstrated experimentally. We proposed an illumination correction method based on fluorescent microscope slides, termed Systematic Uniform Fluorescence Image Correction (SUFIC). And we evaluated SUFIC using the images of fluorescent microspheres, Argo-HM slide, and live cells expressing FRET construct. After SUFIC correction, the field uniformity of the "field of rings" image in Argo-HM slide increased from 27.45% to 65.30%. The signal-to-background ratios of the FRET three-channel images increased by 12.3%, 7.9%, and 20.9%. Compared to the CIDRE and BaSiC methods, which require 100 input images for prospective correction, SUFIC requires only three reference images at minimum. In summary, SUFIC is a highly efficient prospective illumination correction method for quantitative microscopic imaging.

The majority of known methods for correction of multispectral images distorted by nonuniform illumination use the following distortion model: a certain part of the scene close to a directed light source is illuminated much brighter than the rest of the scene. However, another serious problem often arises in practice in the case of nonuniform illumination of 3D objects of the scene: extended heavily shadowed regions with a small area of transition from light to shadow are formed. In this study, a method for the locally adaptive correction of nonuniform illumination of multispectral digital images, which is based on an algorithm that imitates human visual perception, is proposed. The performance of the proposed method is compared to that of available algorithms for correction of color images distorted by both nonuniform illumination and the presence of shadow regions.

Image processing is one of the rapidly growing technologies with operations that can be applied to image data which may be in the form of a 2D, 3D or 4D signals. It has created tremendous opportunities for mathematical modeling, analysis, and computation. A novel approach in image processing has been developed, known as PDE (Partial Differential Equations) based image processing. The PDE approach is very promising for solving many problems in image processing because it provides new and more intuitive mathematical models, gives better approximations to the Euclidean geometry of the problem, and is supported by efficient discrete numerical algorithms based on difference approximations. In this paper, we have discussed how Euler Lagrange Equation plays a significant role in solving PDE based image processing problems. The typical image processing problems such as denoising and inpainting can be solved using EL equation. The ROF and Tikhnov models of denoising and Total Variation based inpainting has been implemented and a comparative study is done with the conventional methods. We have considered various well-known objective quality evaluation metrics used in image processing in this comparison. The results show that PDE based image processing techniques outperforms the conventional approaches.

Absorption and scattering in aqueous media would attenuate light and make imaging difficult. Therefore, an artificial light source is usually utilized to assist imaging in the deep ocean. However, the artificial light source typically alters the light conditions to a large extent, resulting in the non-uniform illumination of images. To solve this problem, we propose a non-uniform illumination correction algorithm based on a fully convolutional network for underwater images. The proposed algorithm model the original image as the addition of the ideal image and a non-uniform light layer. We replace the traditional pooling layer with dilated convolution to expand the receptive field and achieve higher accuracy in non-uniform illumination recognition. To improve the perception ability of the network effectively, the original image and parameters which pre-trained on the ImageNet are concentrated. The concentrated information is used as input to the network. Due to the color shift and blurred details of the underwater image, we design the novel loss function, which includes three parts of feature loss, smooth loss, and adversarial loss. Moreover, we built a dataset of the underwater image with non-uniform illumination. Experiments show that our method performs better in subjective assessment and objective assessment than some traditional methods.

Image registration is amongst the most prominent problems in image processing and computer vision. Particularly in biomedical applications, automated alignment of image data from different imaging modalities has received great attention, delivering a high value added for analysis and diagnosis by integrating spatial information of two or more assays. In this context, the use of entropy based mutual information between images has been widely propagated to capture the relation between differential intensity distributions. In this work we address the problem of matching two different intensity distributions in a supervised learning scenario: We approximate a function relating both intensity distributions using a regression neural network predicting intensity values of one modality to the other, thereby allowing direct intensity difference registration. Predictions are based on a Gabor space representation of the input image, in order to capture local image structures. In experiments we show that the approach is i) able to learn a function to predict intensity values and ii) the predictions can be used to correctly register images by direct intensity differences minimization. The latter has the advantage of being computationally appealing and more stable concerning the optimization framework, which we exploit in registering histological section and NMRi data of plant specimen.

Achieving color constancy between and within images, i.e., minimizing the color difference between the same object imaged under nonuniform and varied illuminations is crucial for computer vision tasks such as colorimetric analysis and object recognition. Most current methods attempt to solve this by illumination correction on perceptual color spaces. In this paper, we proposed two pixel-wise algorithms to achieve relative color constancy by working under the spectral domain. That is, the proposed algorithms map each pixel to the reflectance ratio of objects appeared in the scene and perform illumination correction in this spectral domain. Also, we proposed a camera calibration technique that calculates the characteristics of a camera without the need of a standard reference. We show that both of the proposed algorithms achieved the best performance on nonuniform illumination correction and relative illumination matching respectively compared to the benchmarked algorithms.

Image segmentation is an important problem in image processing that has a wide range of applications in medicine, biomedicine and other fields of science and engineering. During the non-learning-based approaches, the techniques based on the partial differential equations and calculus of variation have attracted a lot of attention and acquired many achievements. Among the variational models, the Chan-Vese variational segmentation is a well-known model to solve the image segmentation problem. The level set methods are highly accurate methods to solve this model, and they do not depend on the edges. However, the performance of these methods depends on the level set function and its initial boundary too much. In this paper, we propose automatic initial boundary generation methods based on the edge detectors: Sobel, Prewitt, Roberts and Canny. In the experiments, we prove that among the four proposed initial boundary generation methods, the method based on the Canny edge detector brings the highest performance for the segmentation method. By combining the proposed initial boundary generation method based on the Canny edge detector, we implement the Chan-Vese model to segment biomedical images. Experimental results indicate we obtain improved segmentation results and compare different edge detectors in terms of performance.

The paper deals with correction of color images distorted by spatially nonuniform illumination. A serious distortion occurs in real conditions when a part of the scene containing 3D objects close to a directed light source is illuminated much brighter than the rest of the scene. A locally-adaptive algorithm for correction of shadow regions in color images is proposed. The algorithm consists of segmentation of shadow areas with rank-order statistics followed by correction of nonuniform illumination with human visual perception approach. The performance of the proposed algorithm is compared to that of common algorithms for correction of color images containing shadow regions.

Robust image segmentation and bias field correction model based on image structural prior constraint

An automatic method for segmenting glottis in high speed endoscopic video (HSV) images of vocal folds is proposed. The method is based on image histogram modeling. Three fundamental problems in automatic histogram based processing of HSV images, which are automatic localization of vocal folds, deformation of the intensity distribution by nonuniform illumination, and ambiguous segmentation when glottal gap is small, are addressed. The problems are solved by using novel masking, illumination, and reflectance modeling methods. The overall algorithm has three stages: masking, illumination modeling, and segmentation. Firstly, a mask is determined based on total variation norm for the region of interest in HSV images. Secondly, a planar illumination model is estimated from consecutive HSV images and reflectance image is obtained. Reflectance images of the masked HSV are used to form a vertical slice image whose reflectance distribution is modeled by a Gaussian mixture model (GMM). Finally, estimated GMM is used to isolate the glottis from the background. Results show that proposed method provides about 94% improvements with respect to manually segmented data in contrast to conventional method which uses Rayleigh intensity distribution in extracting the glottal areas.

In this paper, we provide a new model for simultaneous denoising and illumination correction. A variational framework based on local maximum likelihood estimation (MLE) and a nonlocal regularization is proposed and studied. The proposed minimization problem can be efficiently solved by the augmented Lagrangian method coupled with a maximum expectation step. Experimental results show that our model can provide more homogeneous denoisng results compared to some earlier variational method. In addition, the new method also produces good results under both Gaussian and non-Gaussian noise such as Gaussian mixture, impulse noise and their mixtures.KeywordsNoisy ImageImpulse NoiseAugmented Lagrangian MethodBias FunctionSplit Bregman MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.