Power Law Transformation Research Articles

Digital Image Processing Using Coefficients of Sakaguchi Kind Function Defined in Limacon Shaped Domain with Power Law Transformation

Digital Image Processing Using Coefficients of Sakaguchi Kind Function Defined in Limacon Shaped Domain with Power Law Transformation

Enhanced Power Law Transformation for Histopathology Images of Breast Cancer

Different image enhancement techniques are applied to improve the visual quality of an image on a display device. Contrast stretching, intensity level slicing with and without background, histogram equalization, logarithmic transformation and power law transformation are some image enhancement techniques. Most of the research work focuses on adaptive gamma correcting factors for better visualization of extremely low contrast images, giving less importance to the constant for enhanced visualization. This research proposes an efficient and less complex enhanced power law transformation (EPLT) approach to improve the contrast of dimmed and extremely bright images. The approach is a quick way to compute the value of C, i.e. constant for enhanced visualization. For better picture quality, it is very important to determine C automatically and the gamma correcting factor. This technique offers a novel and unique perspective on image contrast manipulation. The proposed enhancement technique is experimented on histopathology images of breast cancer, bright images and extremely dark images. The average peak signal-to-noise ratio (PSNR) for clinical data and BreakHis dataset is high for the proposed method are 16.52487 and 17.69335 respectively. The average RMSE for clinical data and BreakHis dataset is low for the proposed method are 40.88251 and 44.2546 respectively. It is observed that the proposed method yields the most satisfactory contrast enhancements based on performance comparison with other state-of-art enhancement algorithms and works efficiently on all types of images.

Diabetic retinopathy prediction based on vision transformer and modified capsule network

Diabetic retinopathy is considered one of the most common diseases that can lead to blindness in the working age, and the chance of developing it increases as long as a person suffers from diabetes. Protecting the sight of the patient or decelerating the evolution of this disease depends on its early detection as well as identifying the exact levels of this pathology, which is done manually by ophthalmologists. This manual process is very consuming in terms of the time and experience of an expert ophthalmologist, which makes developing an automated method to aid in the diagnosis of diabetic retinopathy an essential and urgent need. In this paper, we aim to propose a new hybrid deep learning method based on a fine-tuning vision transformer and a modified capsule network for automatic diabetic retinopathy severity level prediction. The proposed approach consists of a new range of computer vision operations, including the power law transformation technique and the contrast-limiting adaptive histogram equalization technique in the preprocessing step. While the classification step builds up on a fine-tuning vision transformer, a modified capsule network, and a classification model combined with a classification model, The effectiveness of our approach was evaluated using four datasets, including the APTOS, Messidor-2, DDR, and EyePACS datasets, for the task of severity levels of diabetic retinopathy. We have attained excellent test accuracy scores on the four datasets, respectively: 88.18%, 87.78%, 80.36%, and 78.64%. Comparing our results with the state-of-the-art, we reached a better performance.

An introduction to double stain normalization technique for brain tumour histopathological images

Stain normalization is an image pre-processing method extensively used to standardize multiple variances of staining intensity in histopathology image analysis. Staining variations may occur for several reasons, such as unstandardized protocols while preparing the specimens, using dyes from different manufacturers, and varying parameters set while capturing the digital images. In this study, a double stain normalization technique based on immunohistochemical staining is developed to improve the performance of the conventional Reinhard’s algorithm. The proposed approach began with preparing a target image by applying the contrast-limited adaptive histogram equalization (CLAHE) technique to the targeted cells. Later, the colour distribution of the input image will be matched to the colour distribution of the target image through the linear transformation process. In this study, the power-law transformation was applied to address the over-enhancement and contrast degradation issues in the conventional method. Five quality metrics comprised of entropy, tenengrad criterion (TEN), mean square error (MSE), structural similarity index (SSIM) and correlation coefficient were used to measure the performance of the proposed system. The experimental results demonstrate that the proposed method outperformed all conventional techniques. The proposed method achieved the highest average values of 5.59, 3854.11 and 94.65 for entropy, TEN, and MSE analyses.

Developing a Colorimetric Equation and a Colorimetric Model to Create a Smartphone Application That Identifies the Ripening Stage of Lady Finger Bananas in Thailand.

This article develops a colorimetric equation and a colorimetric model to create a smartphone application that identifies the ripening stage of the lady finger banana (LFB) (Musa AA group 'Kluai Khai', กล้วยไข่ "gluay kai" in Thai). The mobile application photographs an LFB, automatically analyzes the color of the banana, and tells the user the number of days until the banana ripens and the number of days the banana will remain edible. The application is called the Automatic Banana Ripeness Indicator (ABRI, pronounced like "Aubrey"), and the rapid analysis that it provides is useful to anyone involved in the storage and distribution of bananas. The colorimetric equation interprets the skin color with the CIE L*a*b* color model in conjunction with the Pythagorean theorem. The colorimetric model has three parts. First, COCO-SSD object detection locates and identifies the banana in the image. Second, the Automatic Power-Law Transformation, developed here, adjusts the illumination to a standard derived from the average of a set of laboratory images. After removing the image background and converting the image to L*a*b*, the data are sent to the colorimetric equation to calculate the ripening stage. Results show that ABRI correctly detects a banana with 91.45% accuracy and the Automatic Power-Law Transformation correctly adjusts the image illumination with 95.72% accuracy. The colorimetric equation correctly identifies the ripening stage of all incoming images. ABRI is thus an accurate and robust tool that quickly, conveniently, and reliably provides the user with any LFB's ripening stage and the remaining days for consumption.

Applying a Power Transformation to the Orbit of the 2nd Painleve Equation and Solving Differential Equations with Polynomial Right-hand Sides Via the 2nd Painleve Transcendent and in Polynomials

The 2nd Painleve equation is considered as a representative of the second-order class of ordinary differential equations (ODEs) with polynomial right-hand sides, as well as of the more general second-order class of equations with fractional polynomial right-hand sides. The second Painlevé equation with three terms on the right side has an orbit in the class of fractional polynomial equations with respect to the pseudogroup of the 36th order, and in the absence of the 3rd term – the 60th order. This paper presents a power transformation with an arbitrary parameter that preserves the polynomial or fractional polynomial form of the equations. This power-law transformation is applied to the orbital equations of the 2nd Painlevé equation with three and two terms on the right-hand sides of the equations. Pseudogroups of transformations induced by the above-mentioned pseudogroups of the 36th and 60th orders are constructed. All equations with one-constant arbitrariness corresponding to the vertices of the graphs of induced pseudogroups are found. General solutions of all found equations are obtained through the 2nd Painlevé transcendental or in polynomials. A theorem is presented that allows, using the scaling operation, to find general solutions to all the above equations with arbitrary coefficients.

U-Shaped Low-Complexity Type-2 Fuzzy LSTM Neural Network for Speech Enhancement

Speech enhancement (SE) aims to improve the intelligibility and perceptual quality of speech contaminated by noise signals through spectral or temporal changes. Deep learning models achieve speech enhancement and estimate the magnitude spectrum. This paper proposes a novel and computationally efficient deep learning model to enhance noisy speech. The model pre-processes the noisy speech magnitude by redistributing energy from high-energy voiced segments to low-energy unvoiced segments using an adaptive power law transformation while maintaining the total energy of the speech signals constant. A U-shaped fuzzy long short-term memory (UFLSTM) estimates the magnitude of a time-frequency (T-F) mask by using the pre-processed data. Residual connections to the similar-shaped layers are added to avoid gradient decay. Attention process is adopted by modifying the forget gate of UFLSTM. To make a causal speech enhancement system, the processing does not include any future audio frames. We compare the proposed speech enhancement to other deep learning models in different noisy environments with signal-to-noise ratios of 0 dB, 5 dB, and 10 dB. The experiments show that the proposed SE system outscores the competing deep learning models and considerably improves speech intelligibility and quality. In terms of STOI and PESQ, the LibriSpeech database improves results by (0.211) 21.1% and (0.95) 36.39%, respectively, over noisy speech in seen noisy conditions, and by (0.199) 19.9% and (0.94) 35.69% over noisy speech in unseen noisy conditions. Further, the cross-corpus analysis shows that proposed SE system performs better when trained with the DNS dataset as compared to the LibriSpeech, VoiceBank, and TIMIT datasets.

Robust Ulcer Classification: Contrast and Illumination Invariant Approach.

Gastrointestinal (GI) disease cases are on the rise throughout the world. Ulcers, being the most common type of GI disease, if left untreated, can cause internal bleeding resulting in anemia and bloody vomiting. Early detection and classification of different types of ulcers can reduce the death rate and severity of the disease. Manual detection and classification of ulcers are tedious and error-prone. This calls for automated systems based on computer vision techniques to detect and classify ulcers in images and video data. A major challenge in accurate detection and classification is dealing with the similarity among classes and the poor quality of input images. Improper contrast and illumination reduce the anticipated classification accuracy. In this paper, contrast and illumination invariance was achieved by utilizing log transformation and power law transformation. Optimal values of the parameters for both these techniques were achieved and combined to obtain the fused image dataset. Augmentation was used to handle overfitting and classification was performed using the lightweight and efficient deep learning model MobilNetv2. Experiments were conducted on the KVASIR dataset to assess the efficacy of the proposed approach. An accuracy of 96.71% was achieved, which is a considerable improvement over the state-of-the-art techniques.

A Post-Processing Algorithm for Boosting Contrast of MRI Images

Low contrast of Magnetic Resonance (MR) images limits the visibility of subtle structures and adversely affects the outcome of both subjective and automated diagnosis. State-of-the-art contrast boosting techniques intolerably alter inherent features of MR images. Drastic changes in brightness features, induced by post-processing are not appreciated in medical imaging as the grey level values have certain diagnostic meanings. To overcome these issues this paper proposes an algorithm that enhance the contrast of MR images while preserving the underlying features as well. This method termed as Power-law and Logarithmic Modification-based Histogram Equalization (PLMHE) partitions the histogram of the image into two sub histograms after a power-law transformation and a log compression. After a modification intended for improving the dispersion of the sub-histograms and subsequent normalization, cumulative histograms are computed. Enhanced grey level values are computed from the resultant cumulative histograms. The performance of the PLMHE algorithm is compared with traditional histogram equalization based algorithms and it has been observed from the results that PLMHE can boost the image contrast without causing dynamic range compression, a significant change in mean brightness, and contrast-overshoot.

Image-based Automatic Counting of Bacillus cereus Colonies using Smartphone

Substantial amounts of Bacillus cereus bacteria present in food indicates that the food is unsafe to eat, so counting B. cereus colonies in food samples is a common test for food cleanliness. Manual counting of B. cereus bacteria colonies requires approximately 2-5 minutes per Petri dish, depending on the number of colonies present. This study presents a new smartphone-based method called Bacillus Cereus Image Counting System (BCICS, “B. kiks”) for automatic counting of B. cereus colonies. BCICS uses image processing techniques including Projection Profiling, Circle Hough Transformation, Adaptive Thresholding, and Power-Law Transformation to achieve high image clarity and then uses the Connected-Component Labeling (CCL) technique to correctly count the colonies, including overlapping colonies. These techniques are built into a convenient Android smartphone application. Results of counting the colonies with BCICS were compared with results of hand counting the same dishes. The accuracy rate of each dish count was calculated, as well as the average dish accuracy across all dishes. BCICS counted total colonies with an accuracy of 90.14%, which is close to that of hand counting accuracy since hand counting itself commonly involves an error rate of 5-10%. Importantly, the application took only 3-5 seconds to count one Petri dish, which is more than 74 times faster than the time required for manual counting.

Power law bond price and yield approximation

PurposeThis paper determines a simple transformation that nearly linearizes the bond price formula. The transformed price can be used to derive a highly accurate approximation of the change in a bond price resulting from a change in interest rates.Design/methodology/approachA logarithmic transformation exactly linearizes the price function for a zero coupon bond and a reciprocal transformation exactly linearizes the price function for a perpetuity. A power law transformation combines aspects of both types of transformations and provides a superior approximation of the bond price sensitivity for both short-term and long-term bonds.FindingsIt is demonstrated that the new formula, based on power-law transformation, is a much better approximation than either the traditional duration-convexity approximation and the more recently developed approximations based on logarithmic transformation of the price function.Originality/valueThe new formula will be used by risk managers to perform stress-testing on bond portfolios. The new formula can easily be inverted, making it possible to relate the distribution of prices (which are observable in the market) to the distribution of yields (which are numerical solutions that are not directly observable).

Combined Gray Level Transformation Technique for Low Light Color Image Enhancement

Insufficient and poor lightning conditions affect the quality of videos and images captured by the camcorders. The low quality images decrease the performances of computer vision systems in smart traffic, video surveillance, and other imaging systems applications. In this paper, combined gray level transformation technique is proposed to enhance the less quality of illuminated images. This technique is composed of log transformation, power law transformation and adaptive histogram equalization process to improve the low light illumination image estimated using HIS color model. Finally, the enhanced illumination image is blended with original reflectance image to get enhanced color image. This paper shows that the proposed algorithm on various weakly illuminated images is enhanced better and has taken reduced computation time than previous image processing techniques.

Single-trial detection of EEG error-related potentials using modified power-law transformation

Error processing in the human brain is characterized by a distinct neural response that is elicited when the outcome of an event is not the same as expected. This response is known as error-related potential (ErrP). Detection of error-related potentials from a single-trial data can lead the existing Brain-Computer Interface (BCI) systems one step closer to autonomous system. The non-stationarity of the Electroencephalograph (EEG) signal along with poor spatial resolution and low signal-to-noise ratio make the task of detecting ErrP on a single-trial basis challenging. The objective of this work is to propose a novel ErrP detection method based on temporal domain features of ErrP, particularly, the standard deviation measure. The difference in the standard deviation between the correct and the erroneous trials is verified using a statistical test and this information is subsequently used for ErrP detection. In the proposed method, the EEG electrodes from the frontocentral region of the brain are ranked using standard deviation based ranking criterion and a few top-ranked electrodes will be considered for single-trial detection of ErrP. Then, a modified power-law based transformation is proposed to enhance the discriminability between the correct and error trials. The discriminability is enhanced by transforming the samples lying outside a predefined amplitude range according to power-law equation and the samples within the selected amplitude range are transformed linearly. The modified power-law transformation has two parameters K and γ. The parameter K defines the pre-defined amplitude range and γ is the power in the standard power-law equation. The proposed ErrP detection method is tested on a publicly available EEG database of 10 subjects. The proposed transformation increases the discriminability between the erroneous and correct trials and achieves the best trade-off between the sensitivity and the specificity for detecting ErrP on single-trial basis compared to existing methods. The average sensitivity and specificity achieved is 86.17±9.05% and 92.05±3.69% respectively. The higher sensitivity of detection erroneous trials can be used to faithfully correct the wrongly decoded signal in the EEG based BCI system.

3D color channel based adaptive contrast enhancement using compensated histogram system

Low contrast image is one of the major challenges in photography. The low contrast image not only poses difficulty to the interpretation of the scene but also causes trouble in the onward processing of the image for computer vision tasks. Histogram equalization (HE) is a traditional and widely used approach for contrast enhancement and applies to almost all types of images. However, HE causes over-enhancement of the image which degrades its natural appearance. In this paper, a novel scheme for enhancing the image contrast while retaining its naturalness has been proposed. The proposed method uses the compensated histogram equalization technique on each channel individually followed by blending of the channels with a suitable adaptive brightness adjustment kernel. The three color channels are combined to form the intermediate image. The high-frequency noise introduced during the process is filtered out. Finally, adaptive power law transformation is applied to adjust the overall brightness and to retain its naturalness. This makes the method strong in terms of contrast enhancement along with details preservation. The proposed method is applicable to all the contrast degraded images as it automatically adjusts its parameters based on the degradation level. The simulation results, on the CSIQ dataset, show that the proposed method performs better, qualitatively, and quantitatively than the existing methods.

Transfer Learning approach for grading of Diabetic Retinopathy

There has been a wide interest in applying Deep Learning (DL) algorithms for automated binary and multi class classification of colour fundus images affected with Diabetic Retinopathy (DR). These algorithms have shown high sensitivity and specificity for detecting DR in non-clinical setup. Transfer learning has been successfully tested in many medical imaging applications like skin cancer detection, pulmonary nodule detection, Alzheimer’s disease etc. This paper experiments with the different DL architectures such as VGG19, InceptionV3, ResNet50, MobileNet and NASNet for automated DR classification (binary and multi class) on Messidor dataset. The dataset is publicly available, and comprises of 1200 retinal fundus images. The images belong to four different classes of DR namely, normal (class 0), mild (class 1), moderate (class 2) and severe (class 3), graded based on the severity level of DR. In our experiment, we have enhanced the quality of input images by applying algorithms like CLAHE (Contrast Limited Adaptive Histogram Equalisation) algorithm and Powerlaw transformation as pre-processing techniques, which work on the small image patches with high accuracy, contrast limiting and image sharpening. Hyper parameter tuning on pretrained InceptionV3 architecture, resulted in enhancing the accuracy of the model. Both binary and multi class results were analysed considering inter class (one class with another class) accuracies. We achieved an accuracy of 78% between class 0 and class 1, the accuracy between class 0 and class 2 further reduced to 69%, while class 1 and class 2 showed an accuracy of 61%. Moreover, the interclass class accuracy between class 1 and class 3 was 62%, class 2 and class 3 further reduced to 49%. The accuracy further diminished between class 0 and class 3 to 32%. These experiments suggest that the pretrained models provided better results in classifying normal and mild, but they were not that much efficient in classifying moderate-severe and normal-severe binary classifications.

Space-time processing for «range – azimuth – elevation» measurements in non-cooperative systems of radars with phased array antennas

The methods of measuring the three coordinates of an aircraft in the takeoff and landing mode on the runway of airfields based on the use of non - cooperative two-and three-position systems of radars with phased array antennas are considered. For these variants, general analytical expressions are obtained for the complex generalized correlation integral of space – time processing in the function of spatial coordinates, taking into account the individual directional pattern of phased array antennas. On the basis of two – dimensional profiles of the correlation integral modules «range – elevation» and «azimuth – elevation», examples of comparing particular variants of two-position and three-position systems of radars with their location on one straight line parallel runway are given. In conditions of large signal-to-noise ratios, power-law nonlinear transformations of the correlation integral correlation integral module are applied to reduce the level of side lobes in the two – dimensional sections «range – elevation» and «azimuth – elevation». The following results are obtained using examples. Two-dimensional diagrams of the correlation integral module «range – elevation» do not depend on the azimuth of the aircraft in the range of azimuth values β=0…10 ̊ and correctly display the angle of elevation and the range of the aircraft when 2…3 radars of a non-cooperative system are located on the straight line parallel runway. The two-dimensional diagrams of the correlation integral module «azimuth – elevation angle» have an interference structure, and the number and level of their side lobes increase with increasing azimuth of the aircraft. With azimuth β≥10 ̊, this can lead to ambiguity in the measurement of the azimuth and uncertainty in the elevation angle . One of the measures to reduce the side level of the diagrams of the correlation integral module can be the use of a power-law transformation of normalized diagrams exponentiation of degree 3...4. An increase in the number of radars from two to three when they are located on one straight line parallel to the runway led to a decrease in the side lobes level of the «range – elevation angle» and «azimuth – elevation angle» diagrams. In this case, it may be advisable to solve the problem of optimal choice of the position of the intermediate radar on the same straight line. Calculations were also carried out for an additional example of the location of the intermediate radar of a 3-position system with its removal from the base line. At the same time, there was an increase of the side lobes level in the «azimuth – elevation angle» sections, which in the future may require additional research in terms of optimizing the placement of the radars in horizontal plane for such a radar systems.

FEEG Contrast Enhancement: Power Law Transformation vs Intuitionistic Fuzzy Set

This work focused on contrast enhancement of Flat Electroencephalography (fEEG) image by using Power Law Transformation (PLT) and Intuitionistic Fuzzy Set (IFS). PLT is a classical method whereas the IFS is an advanced fuzzy approach. The values of parameter in both methods are varied to obtain different levels of enhancement. The results show that the IFS is more powerful in preserving the information of the cluster centresas the values of parameter increased.

WITHDRAWN: Low light image contrast enhancement using advanced perfusion technique

Abstract The images captured tend to degrade due to the scattering and absorption of light. This may be due to the diminished colors, low light and undistinguishable objects in the image. For the improvement of quality of such degraded images, Advanced Perfusion technique is employed to enhance the contrast of the low light Image. In this technique, the input image in RGB color space is converted to LAB color spaces. Two versions of input image are considered, in which, the first image is processed for brightness contrast enhancement and the second image is processed for color contrast enhancement. For the enhancement of color contrast, the second image is passed through a Recursive Separated and Weighted Histogram Equalization, (RSWHE) followed by power law transformation. Two main features are extracted from both the images, namely, Laplacian weight map and Saliency weight map. These two features of the two LAB images are fused together to produce a final enhanced image, which has improved brightness contrast and color contrast. The proposed image enhancement technique is evaluated with various performance parameters such as Structural Similarity Index (SSIM), Peak Signal-to-Noise Ratio (PSNR), and Lightness Order Error (LOE). The performance of the proposed method is then compared with the existing methods for validation.

Image Enhancement Using Wavelet Based Image Fusion and Power Law Transform

One of the best branches of data fusion is Image Fusion and Power law transform is having its own importance in image enhancement. The future applications will be mainly based on image brightness and image sharpness. The enhanced images provide better information than the low-quality blur images. In this paper, we acquired a solitary image which introduces better execution under a few assessment criteria’s by combining wavelet transform with power law transformation for the images at around various locales. Wavelet transform is basically utilized as a result of its natural property that is, they are repetitive and move variation. It changes image into various scales. In power law transformation one must pick the example showing up in the transform capacity with the end goal that it doesn’t corrupt the nature of the image. The empirical results are better for proposed algorithm compare with state of art algorithms.

A Deep Learning Based Method for Detecting of Wear on the Current Collector Strips’ Surfaces of the Pantograph in Railways

In pantographs, current collector strips transmit the electrical energy they receive from the catenary to the locomotive and provide the necessary power for the locomotive's movement. In order for the current collector strips to transmit electricity to the locomotive in a healthy way, their surface must be smooth. Wear on the surface of the current collector strips reduces conductivity and can create arcs, endangering the health and safety of the pantograph and catenary system. In this paper, a Convolutional Neural Network (CNN) architecture is developed to detect wear on the current collector strips. Images obtained from pantographs used on railways were created with a clean and improved data set using Hough Transform and Power Law Transform. The created dataset contains 909 pantograph images. This dataset was trained and tested with both the developed CNN architecture and classic deep learning architectures (ResNet50, VGG16). The experimental results show that the developed CNN architecture's training results and test results are more successful than classical architectures.