Search results for: Gradient image

Authors: S. Sowmyayani, V. Murugan

Abstract:

With the advent of three-dimension (3D) technology, there are lots of research in converting 2D images to 3D images. The main difference between 2D and 3D is the visual illusion of depth in 3D images. In the recent era, there are more depth estimation techniques. The objective of this paper is to convert 2D images to 3D images with less computation time. For this, the input image is divided into blocks from which the depth information is obtained. Having the depth information, a depth map is generated. Then the 3D image is warped using the original image and the depth map. The proposed method is tested on Make3D dataset and NYU-V2 dataset. The experimental results are compared with other recent methods. The proposed method proved to work with less computation time and good accuracy.

Keywords: Depth map, 3D image warping, image rendering, bilateral filter, minimum spanning tree.

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Authors: Pil Un Kim, Yunjung Lee, Gihyoun Lee, Jin Ho Cho, Myoung Nam Kim

Abstract:

In this paper, the vessel inscribed trigonometry (VITM) for the vessel progression orientation (VPO) is proposed in the two-dimensional fundus image. The VPO is a major factor in the optic disc (OD) detection which is a basic process in the retina analysis. To measure the VPO, skeletons of vessel are used. First, the vessels are classified into three classes as vessel end, vessel branch and vessel stem. And the chain code maps of VS are generated. Next, two farthest neighborhoods of each point on VS are searched by the proposed angle restriction. Lastly, a gradient of the straight line between two farthest neighborhoods is estimated to measure the VPO. VITM is validated by comparing with manual results and 2D Gaussian templates. It is confirmed that VPO of the proposed mensuration is correct enough to detect OD from the results of experiment which applied VITM to detect OD in fundus images.

Keywords: Angle measurement, Optic disc, Retina vessel, Vessel progression orientation.

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Authors: Khalid A. Al-Afandy, El-Sayyed El-Rabaie, Osama Salah, Ahmed El-Mhalaway

Abstract:

This paper presents a high secure data hiding technique using image cropping and Least Significant Bit (LSB) steganography. The predefined certain secret coordinate crops will be extracted from the cover image. The secret text message will be divided into sections. These sections quantity is equal the image crops quantity. Each section from the secret text message will embed into an image crop with a secret sequence using LSB technique. The embedding is done using the cover image color channels. Stego image is given by reassembling the image and the stego crops. The results of the technique will be compared to the other state of art techniques. Evaluation is based on visualization to detect any degradation of stego image, the difficulty of extracting the embedded data by any unauthorized viewer, Peak Signal-to-Noise Ratio of stego image (PSNR), and the embedding algorithm CPU time. Experimental results ensure that the proposed technique is more secure compared with the other traditional techniques.

Keywords: Steganography, stego, LSB, crop.

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Authors: Maha Sharkas, Dahlia ElShafie, Nadder Hamdy

Abstract:

Image watermarking has become an important tool for intellectual property protection and authentication. In this paper a watermarking technique is suggested that incorporates two watermarks in a host image for improved protection and robustness. A watermark, in form of a PN sequence (will be called the secondary watermark), is embedded in the wavelet domain of a primary watermark before being embedded in the host image. The technique has been tested using Lena image as a host and the camera man as the primary watermark. The embedded PN sequence was detectable through correlation among other five sequences where a PSNR of 44.1065 dB was measured. Furthermore, to test the robustness of the technique, the watermarked image was exposed to four types of attacks, namely compression, low pass filtering, salt and pepper noise and luminance change. In all cases the secondary watermark was easy to detect even when the primary one is severely distorted.

Keywords: DWT, Image watermarking, watermarkingtechniques, wavelets.

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Authors: G. Sadashivappa, K. V. S. AnandaBabu

Abstract:

The aim of this paper to characterize a larger set of wavelet functions for implementation in a still image compression system using SPIHT algorithm. This paper discusses important features of wavelet functions and filters used in sub band coding to convert image into wavelet coefficients in MATLAB. Image quality is measured objectively using peak signal to noise ratio (PSNR) and its variation with bit rate (bpp). The effect of different parameters is studied on different wavelet functions. Our results provide a good reference for application designers of wavelet based coder.

Keywords: Wavelet, image compression, sub band, SPIHT, PSNR.

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Authors: Rehab H. Alwan, Fadhil J. Kadhim, Ahmad T. Al-Taani

Abstract:

In this study, a novel approach of image embedding is introduced. The proposed method consists of three main steps. First, the edge of the image is detected using Sobel mask filters. Second, the least significant bit LSB of each pixel is used. Finally, a gray level connectivity is applied using a fuzzy approach and the ASCII code is used for information hiding. The prior bit of the LSB represents the edged image after gray level connectivity, and the remaining six bits represent the original image with very little difference in contrast. The proposed method embeds three images in one image and includes, as a special case of data embedding, information hiding, identifying and authenticating text embedded within the digital images. Image embedding method is considered to be one of the good compression methods, in terms of reserving memory space. Moreover, information hiding within digital image can be used for security information transfer. The creation and extraction of three embedded images, and hiding text information is discussed and illustrated, in the following sections.

Keywords: Image embedding, Edge detection, gray level connectivity, information hiding, digital image compression.

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Authors: A. Elyousfi, A. Tamtaoui, E. Bouyakhf

Abstract:

The H.264/AVC standard uses an intra prediction, 9 directional modes for 4x4 luma blocks and 8x8 luma blocks, 4 directional modes for 16x16 macroblock and 8x8 chroma blocks, respectively. It means that, for a macroblock, it has to perform 736 different RDO calculation before a best RDO modes is determined. With this Multiple intra-mode prediction, intra coding of H.264/AVC offers a considerably higher improvement in coding efficiency compared to other compression standards, but computational complexity is increased significantly. This paper presents a fast intra prediction algorithm for H.264/AVC intra prediction based a characteristic of homogeneity information. In this study, the gradient prediction method used to predict the homogeneous area and the quadratic prediction function used to predict the nonhomogeneous area. Based on the correlation between the homogeneity and block size, the smaller block is predicted by gradient prediction and quadratic prediction, so the bigger block is predicted by gradient prediction. Experimental results are presented to show that the proposed method reduce the complexity by up to 76.07% maintaining the similar PSNR quality with about 1.94%bit rate increase in average.

Keywords: Intra prediction, H.264/AVC, video coding, encodercomplexity.

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Authors: Yong-Gyu Lee, Gilwon Yoon

Abstract:

Bleeding in the digestive duct is an important diagnostic parameter for patients. Blood in the endoscopic image can be determined by investigating the color tone of blood due to the degree of oxygenation, under- or over- illumination, food debris and secretions, etc. However, we found that how to pre-process raw images obtained from the capsule detectors was very important. We applied various image process methods suitable for the capsule endoscopic image in order to remove noises and unbalanced sensitivities for the image pixels. The results showed that much improvement was achieved by additional pre-processing techniques on the algorithm of determining bleeding areas.

Keywords: blood detection, capsule endoscopy, image processing.

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Authors: Jiann-Ming Wu, Hsiao-Chang Chen, Chun-Chang Wu, Pei-Hsun Hsu

Abstract:

This work explores blind image deconvolution by recursive function approximation based on supervised learning of neural networks, under the assumption that a degraded image is linear convolution of an original source image through a linear shift-invariant (LSI) blurring matrix. Supervised learning of neural networks of radial basis functions (RBF) is employed to construct an embedded recursive function within a blurring image, try to extract non-deterministic component of an original source image, and use them to estimate hyper parameters of a linear image degradation model. Based on the estimated blurring matrix, reconstruction of an original source image from a blurred image is further resolved by an annealed Hopfield neural network. By numerical simulations, the proposed novel method is shown effective for faithful estimation of an unknown blurring matrix and restoration of an original source image.

Keywords: Blind image deconvolution, linear shift-invariant(LSI), linear image degradation model, radial basis functions (rbf), recursive function, annealed Hopfield neural networks.

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Authors: Siraa Ben Ftima, Mourad Talbi, Tahar Ezzedine

Abstract:

In this paper, we present a technique of secure watermarking of grayscale and color images. This technique consists in applying the Singular Value Decomposition (SVD) in LWT (Lifting Wavelet Transform) domain in order to insert the watermark image (grayscale) in the host image (grayscale or color image). It also uses signature in the embedding and extraction steps. The technique is applied on a number of grayscale and color images. The performance of this technique is proved by the PSNR (Pick Signal to Noise Ratio), the MSE (Mean Square Error) and the SSIM (structural similarity) computations.

Keywords: Color image, grayscale image, singular values decomposition, lifting wavelet transform, image watermarking, watermark, secure.

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Authors: K. Suganya Devi, P. Srinivasan, M. P. Vaishnave, G. Arutperumjothi

Abstract:

Today’s internet world is highly prone to various online attacks, of which the most harmful attack is phishing. The attackers host the fake websites which are very similar and look alike. We propose an image based authentication using steganography and visual cryptography to prevent phishing. This paper presents a secure steganographic technique for true color (RGB) images and uses Discrete Cosine Transform to compress the images. The proposed method hides the secret data inside the cover image. The use of visual cryptography is to preserve the privacy of an image by decomposing the original image into two shares. Original image can be identified only when both qualified shares are simultaneously available. Individual share does not reveal the identity of the original image. Thus, the existence of the secret message is hard to be detected by the RS steganalysis.

Keywords: Image security, random LSB, steganography, visual cryptography.

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Authors: Rosa Nurtazina, Yerkebulan Zhumashov, Maral Tomanova

Abstract:

Humanity is entering an era when "virtual reality" as the image of the world created by the media with the help of the Internet does not match the reality in many respects, when new communication technologies create a fundamentally different and previously unknown "global space". According to these technologies, the state begins to change the basic technology of political communication of the state and society, the state and the state. Nowadays image of the state becomes the most important tool and technology.

Image is a purposefully created image granting political object (person, organization, country, etc.) certain social and political values and promoting more emotional perception.

Political image of the state plays an important role in international relations. The success of the country's foreign policy, development of trade and economic relations with other countries depends on whether it is positive or negative. Foreign policy image has an impact on political processes taking place in the state: the negative image of the country's can be used by opposition forces as one of the arguments to criticize the government and its policies.

Keywords: Image of the country, country's image classification, function of the country image, country's image components.

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Authors: Yasser F. Hassan

Abstract:

The reduction or removal of noise in a color image is an essential part of image processing, whether the final information is used for human perception or for an automatic inspection and analysis. This paper describes the modeling system based on the rough neural network model to adaptive cellular automata for various image processing tasks and noise remover. In this paper, we consider the problem of object processing in colored image using rough neural networks to help deriving the rules which will be used in cellular automata for noise image. The proposed method is compared with some classical and recent methods. The results demonstrate that the new model is capable of being trained to perform many different tasks, and that the quality of these results is comparable or better than established specialized algorithms.

Keywords: Rough Sets, Rough Neural Networks, Cellular Automata, Image Processing.

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Authors: Fathi M. O. Hamed, Salma F. Elkofhaifee

Abstract:

The aim of this work is to detect geometrical shape objects in an image. In this paper, the object is considered to be as a circle shape. The identification requires find three characteristics, which are number, size, and location of the object. To achieve the goal of this work, this paper presents an algorithm that combines from some of statistical approaches and image analysis techniques. This algorithm has been implemented to arrive at the major objectives in this paper. The algorithm has been evaluated by using simulated data, and yields good results, and then it has been applied to real data.

Keywords: Image processing, median filter, projection, scalespace, segmentation, threshold.

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Authors: Zhifeng Kong

Abstract:

Over-parameterized neural networks have attracted a great deal of attention in recent deep learning theory research, as they challenge the classic perspective of over-fitting when the model has excessive parameters and have gained empirical success in various settings. While a number of theoretical works have been presented to demystify properties of such models, the convergence properties of such models are still far from being thoroughly understood. In this work, we study the convergence properties of training two-hidden-layer partially over-parameterized fully connected networks with the Rectified Linear Unit activation via gradient descent. To our knowledge, this is the first theoretical work to understand convergence properties of deep over-parameterized networks without the equally-wide-hidden-layer assumption and other unrealistic assumptions. We provide a probabilistic lower bound of the widths of hidden layers and proved linear convergence rate of gradient descent. We also conducted experiments on synthetic and real-world datasets to validate our theory.

Keywords: Over-parameterization, Rectified Linear Units (ReLU), convergence, gradient descent, neural networks.

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Authors: Shimal Das, Dibyendu Ghoshal

Abstract:

Fractal based digital image compression is a specific technique in the field of color image. The method is best suited for irregular shape of image like snow bobs, clouds, flame of fire; tree leaves images, depending on the fact that parts of an image often resemble with other parts of the same image. This technique has drawn much attention in recent years because of very high compression ratio that can be achieved. Hybrid scheme incorporating fractal compression and speedup techniques have achieved high compression ratio compared to pure fractal compression. Fractal image compression is a lossy compression method in which selfsimilarity nature of an image is used. This technique provides high compression ratio, less encoding time and fart decoding process. In this paper, fractal compression with quad tree and DCT is proposed to compress the color image. The proposed hybrid schemes require four phases to compress the color image. First: the image is segmented and Discrete Cosine Transform is applied to each block of the segmented image. Second: the block values are scanned in a zigzag manner to prevent zero co-efficient. Third: the resulting image is partitioned as fractals by quadtree approach. Fourth: the image is compressed using Run length encoding technique.

Keywords: Fractal coding, Discrete Cosine Transform, Iterated Function System (IFS), Affine Transformation, Run length encoding.

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Authors: Abdul Kadir Jumaat, Siti Salmah Yasiran, Wan Eny Zarina Wan Abd Rahman, Aminah Abdul Malek

Abstract:

A mammography image is composed of low contrast area where the breast tissues and the breast abnormalities such as microcalcification can hardly be differentiated by the medical practitioner. This paper presents the application of active contour models (Snakes) for the segmentation of microcalcification in mammography images. Comparison on the microcalcifiation areas segmented by the Balloon Snake, Gradient Vector Flow (GVF) Snake, and Distance Snake is done against the true value of the microcalcification area. The true area value is the average microcalcification area in the original mammography image traced by the expert radiologists. From fifty images tested, the result obtained shows that the accuracy of the Balloon Snake, GVF Snake, and Distance Snake in segmenting boundaries of microcalcification are 96.01%, 95.74%, and 95.70% accuracy respectively. This implies that the Balloon Snake is a better segmentation method to locate the exact boundary of a microcalcification region.

Keywords: Balloon Snake, GVF Snake, Distance Snake, Mammogram, Microcalcifications, Segmentation

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Authors: Mehdi Ghayoumi

Abstract:

We have applied new accelerated algorithm for linear discriminate analysis (LDA) in face recognition with support vector machine. The new algorithm has the advantage of optimal selection of the step size. The gradient descent method and new algorithm has been implemented in software and evaluated on the Yale face database B. The eigenfaces of these approaches have been used to training a KNN. Recognition rate with new algorithm is compared with gradient.

Keywords: lda, adaptive, svm, face recognition.

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Authors: Danni Cong, Meiping Wu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokuncai, Hao Qin

Abstract:

Gravity gradient instrument (GGI) is the core of the gravity gradiometer, so the structural error of the sensor has a great impact on the measurement results. In order not to affect the aimed measurement accuracy, limit error is required in the installation of the accelerometer. In this paper, based on the established measuring principle model, the radial installation limit error is calibrated, which is taken as an example to provide a method to calculate the other limit error of the installation under the premise of ensuring the accuracy of the measurement result. This method provides the idea for deriving the limit error of the geometry structure of the sensor, laying the foundation for the mechanical precision design and physical design.

Keywords: Gravity gradient sensor, radial installation limit error, accelerometer, uniaxial rotational modulation.

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Authors: Iau-Teh Wang, Chin-Yu Lee

Abstract:

The impact force of a rockfall is mainly determined by its moving behavior and velocity, which are contingent on the rock shape, slope gradient, height, and surface roughness of the moving path. It is essential to precisely calculate the moving path of the rockfall in order to effectively minimize and prevent damages caused by the rockfall. By applying the Colorado Rockfall Simulation Program (CRSP) program as the analysis tool, this research studies the influence of three shapes of rock (spherical, cylindrical and discoidal) and surface roughness on the moving path of a single rockfall. As revealed in the analysis, in addition to the slope gradient, the geometry of the falling rock and joint roughness coefficient ( JRC ) of the slope are the main factors affecting the moving behavior of a rockfall. On a single flat slope, both the rock-s bounce height and moving velocity increase as the surface gradient increases, with a critical gradient value of 1:m = 1 . Bouncing behavior and faster moving velocity occur more easily when the rock geometry is more oval. A flat piece tends to cause sliding behavior and is easily influenced by the change of surface undulation. When JRC <1.4 the moving velocity decreases and the bounce height increases as JRC increases. If the gradient is fixed, when JRC is greater, the bounce height will be higher, while the moving velocity will experience a downward trend. Therefore, the best protecting point and facilities can be chosen if the moving paths of rockfalls are precisely estimated.

Keywords: rock shape, surface roughness, moving path.

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Authors: Amarunnishad T.M., Govindan V.K., Abraham T. Mathew

Abstract:

An image compression method has been developed using fuzzy edge image utilizing the basic Block Truncation Coding (BTC) algorithm. The fuzzy edge image has been validated with classical edge detectors on the basis of the results of the well-known Canny edge detector prior to applying to the proposed method. The bit plane generated by the conventional BTC method is replaced with the fuzzy bit plane generated by the logical OR operation between the fuzzy edge image and the corresponding conventional BTC bit plane. The input image is encoded with the block mean and standard deviation and the fuzzy bit plane. The proposed method has been tested with test images of 8 bits/pixel and size 512×512 and found to be superior with better Peak Signal to Noise Ratio (PSNR) when compared to the conventional BTC, and adaptive bit plane selection BTC (ABTC) methods. The raggedness and jagged appearance, and the ringing artifacts at sharp edges are greatly reduced in reconstructed images by the proposed method with the fuzzy bit plane.

Keywords: Image compression, Edge detection, Ground truth image, Peak signal to noise ratio

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Authors: Say Wei Foo, Qi Dong

Abstract:

Digital watermarking has become an important technique for copyright protection but its robustness against attacks remains a major problem. In this paper, we propose a normalizationbased robust image watermarking scheme. In the proposed scheme, original host image is first normalized to a standard form. Zernike transform is then applied to the normalized image to calculate Zernike moments. Dither modulation is adopted to quantize the magnitudes of Zernike moments according to the watermark bit stream. The watermark extracting method is a blind method. Security analysis and false alarm analysis are then performed. The quality degradation of watermarked image caused by the embedded watermark is visually transparent. Experimental results show that the proposed scheme has very high robustness against various image processing operations and geometric attacks.

Keywords: Image watermarking, Image normalization, Zernike moments, Robustness.

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Authors: Faruq A. Al-Omari, Nabeel I. Al-Fayoumi

Abstract:

In this paper, we present a new algorithm for clustering data in large datasets using image processing approaches. First the dataset is mapped into a binary image plane. The synthesized image is then processed utilizing efficient image processing techniques to cluster the data in the dataset. Henceforth, the algorithm avoids exhaustive search to identify clusters. The algorithm considers only a small set of the data that contains critical boundary information sufficient to identify contained clusters. Compared to available data clustering techniques, the proposed algorithm produces similar quality results and outperforms them in execution time and storage requirements.

Keywords: Data clustering, Data mining, Image-mapping, Pattern discovery, Predictive analysis.

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Authors: Mario Mastriani, Juliana Gambini

Abstract:

In this work, we present a comparison between two techniques of image compression. In the first case, the image is divided in blocks which are collected according to zig-zag scan. In the second one, we apply the Fast Cosine Transform to the image, and then the transformed image is divided in blocks which are collected according to zig-zag scan too. Later, in both cases, the Karhunen-Loève transform is applied to mentioned blocks. On the other hand, we present three new metrics based on eigenvalues for a better comparative evaluation of the techniques. Simulations show that the combined version is the best, with minor Mean Absolute Error (MAE) and Mean Squared Error (MSE), higher Peak Signal to Noise Ratio (PSNR) and better image quality. Finally, new technique was far superior to JPEG and JPEG2000.

Keywords: Fast Cosine Transform, image compression, JPEG, JPEG2000, Karhunen-Loève Transform, zig-zag scan.

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Authors: Ting-Chao Chen, Yean-Ren Hwang, Jing-Chie Lin

Abstract:

A real time image-guided electroplating system is proposed in this paper. Unlike previous electroplating systems, instead of using the intermittent mode to electroplate 500um long copper specimen, a CCD camera and a motion controller are used to adjust anode-cathode distance to obtain better results. Since the image of the gap distance is highly deteriorated due to complex chemical-electrical operation inside the electrolyte, to determine the gap distance, an image processing algorithm is developed and mainly based on the entropy and energy values. In addition, the color and incidence direction of light source are also discussed to help the image process in this paper. From the experiment results, the specimens created by the proposed system show better structure, better uniformity and better finishing surface compared to those by previous intermittent electroplating setup.

Keywords: Electroplating, image guided, image process, light source.

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Authors: Mahmoud Elmezain, Ayoub Al-Hamadi, Robert Niese, Bernd Michaelis

Abstract:

Real-time hand tracking is a challenging task in many computer vision applications such as gesture recognition. This paper proposes a robust method for hand tracking in a complex environment using Mean-shift analysis and Kalman filter in conjunction with 3D depth map. The depth information solve the overlapping problem between hands and face, which is obtained by passive stereo measuring based on cross correlation and the known calibration data of the cameras. Mean-shift analysis uses the gradient of Bhattacharyya coefficient as a similarity function to derive the candidate of the hand that is most similar to a given hand target model. And then, Kalman filter is used to estimate the position of the hand target. The results of hand tracking, tested on various video sequences, are robust to changes in shape as well as partial occlusion.

Keywords: Computer Vision and Image Analysis, Object Tracking, Gesture Recognition.

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Authors: El Asnaoui Khalid, Aksasse Brahim, Ouanan Mohammed

Abstract:

This paper presents an unsupervised color image segmentation method. It is based on a hierarchical analysis of 2-D histogram in RGB color space. This histogram minimizes storage space of images and thus facilitates the operations between them. The improved segmentation approach shows a better identification of objects in a color image and, at the same time, the system is fast.

Keywords: Image segmentation, hierarchical analysis, 2-D histogram, Classification.

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Authors: Chang-Hsing Lee, Cheng-Chang Lien, Chin-Chuan Han

Abstract:

In this paper, an edge-strength guided multiscale retinex (EGMSR) approach will be proposed for color image contrast enhancement. In EGMSR, the pixel-dependent weight associated with each pixel in the single scale retinex output image is computed according to the edge strength around this pixel in order to prevent from over-enhancing the noises contained in the smooth dark/bright regions. Further, by fusing together the enhanced results of EGMSR and adaptive multiscale retinex (AMSR), we can get a natural fused image having high contrast and proper tonal rendition. Experimental results on several low-contrast images have shown that our proposed approach can produce natural and appealing enhanced images.

Keywords: Image Enhancement, Multiscale Retinex, Image Fusion.

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Authors: Anastasia Rita Widiarti, Agus Harjoko, Marsono, Sri Hartati

Abstract:

This paper presents the results of a study to test whether the Javanese character manuscript image preprocessing model that have been more widely applied, can also be applied to segment of the Batak characters manuscripts. The treatment process begins by converting the input image into a binary image. After the binary image is cleaned of noise, then the segmentation lines using projection profile is conducted. If unclear histogram projection is found, then the smoothing process before production indexes line segments is conducted. For each line image which has been produced, then the segmentation scripts in the line is applied, with regard of the connectivity between pixels which making up the letters that there is no characters are truncated. From the results of manuscript preprocessing system prototype testing, it is obtained the information about the system truth percentage value on pieces of Pustaka Batak Podani Ma AjiMamisinon manuscript ranged from 65% to 87.68% with a confidence level of 95%. The value indicates the truth percentage shown the initial processing model in Javanese characters manuscript image can be applied also to the image of the Batak characters manuscript.

Keywords: Connected component, preprocessing manuscript image, projection profiles.

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Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

Abstract:

Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: Convergence, iteration, line search, running time, steepest descent, unconstrained optimization.

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