Teruya Minamoto

A blind digital image watermarking method based on the dyadic wavelet transform and interval arithmetic

We propose a new blind digital image watermarking method based on the dyadic wavelet transform (DYWT) and interval arithmetic (IA). Because the DYWT has a redundant representation, the amount of information that the watermark must contain is greater than in the case of the methods based on the ordinary discrete wavelet transforms. Our watermark is a ternary-valued logo that is embedded into the high-frequency components through use of the DYWT and IA. We describe the properties of the DYWT based on IA (IDYWT) and its computational method. We also describe our watermarking procedure in detail and present experimental results demonstrating that our method produces watermarked images that have better quality and are robust with respect to attacks on the following types: marking, clipping, median filtering, contrast tuning (histeq and imadjust commands in the MATLAB Image Processing Toolbox), addition of Gaussian white noise, addition of salt & pepper noise, JPEG and JPEG2000 compressions, rotation, resizing.

A numerical verification method for a periodic solution of a delay differential equation

We describe a numerical method with guaranteed accuracy to enclose a periodic solution for a system of delay differential equations. Using a certain system of equations corresponding to the original system, we derive sufficient conditions for the existence of the solution, the satisfaction of which can be verified computationally. We describe the verification procedure in detail and give a numerical example.

Edge-preserving Image Denoising Method Based on Dyadic Lifting Schemes

In this paper, we propose a new wavelet denoising method with edge preservation for digital images. Traditionally, most denoising methods assume additive Gaussian white noise or statistical models; however, we do not make such an assumption here. Briefly, the proposed method consists of a combination of dyadic lifting schemes and edge-preserving wavelet thresholding. The dyadic lifting schemes have free parameters, enabling us to construct filters that preserve important image features. Our method involves learning such free parameters based on some training images with and without noise. The learnt wavelet filters preserve important features of the original training image while removing noise from noisy images. We describe how to determine these parameters and the edge-preserving denoising algorithm in detail. Numerical image denoising experiments demonstrate the high performance of our method.

A Digital Image Watermarking Method Using Interval Arithmetic

In this letter, we propose a new digital image watermarking method using interval arithmetic. This is a new application of interval arithmetic. Experimental results show that the proposed method gives a watermarked image of better quality and is robust against some attacks.

Numerical existence and uniqueness proof for solutions of semilinear parabolic equations

We describe a numerical method to verify the existence and local uniqueness of solutions of semilinear parabolic equations. We present a detailed description of the verification procedure and determine error bounds for its computation. Several examples are given.

A Non-blind Digital Image Watermarking Method Based on the Dual-tree Complex Discrete Wavelet Transform and Interval Arithmetic

We present a new non-blind digital image watermarking method for embedding a binary logo in an image, based on the dual-tree complex discrete wavelet transform (DT-CDWT) and interval arithmetic (IA). As our experimental results demonstrated, since the high-frequency components obtained by using DT-CDWT and IA contained a low-frequency component, we may expect that the image quality and robustness is maintained even if we embed the watermark into the high-frequency components. A watermark was embedded in several high-frequency components. We describe our watermarking procedure in detail and report experimental results demonstrating that our method gives watermarked images that have better quality and that are robust against attacks such as marking, clipping, contrast tuning (MATLAB histeq and imadjust commands), addition of Gaussian white noise, addition of salt & pepper noise, JPEG and JPEG2000 compression, and rotation.

Computer-Aided Diagnosis Method for Detecting Early Esophageal Cancer from Endoscopic Image by Using Dyadic Wavelet Transform and Fractal Dimension

We propose a new computer-aided method for diagnosing early esophageal cancer from endoscopic images by using the dyadic wavelet transform (DYWT) and the fractal dimension. In our method, an input image is converted into HSV color space, and a fusion image is made from the S (saturation) and V (value) components based on the DYWT. We apply the contrast enhancement to produce a grayscale image in which the structure of abnormal regions is enhanced. We can obtain binary images composed of multiple layers by low-gradation processing. We visualize abnormal regions by summing these fractal dimensions by computing the complexity of these images. We describe a process for enhancing, detecting and visualizing abnormal regions in detail, and we present experimental results demonstrating that our method gives visualized images in which abnormal regions in endoscopic images can be located and that contain data useful for actual diagnosis of early esophageal cancer.

Automatic Detection of Early Esophageal Cancer from Endoscope Image Using Fractal Dimension and Discrete Wavelet Transform

We propose a new method for automatically detecting early esophageal cancer from an endoscopic image. We decompose the original image into four components, namely, the RGB and luminance components, and apply the discrete wavelet transform (DWT) to these components twice. The fractal dimensions are computed at each small block using the box-counting method, and the abnormal regions are detected based on the fractal dimensions. In addition, to process the endoscopic image quickly, we clip the portion that does not contain the esophageal cancer from the original endoscopic image and resize the remaining image to 1024 x 1024 pixels by mirroring. Finally, we show the abnormal region by using the product of the computed fractal dimensions from the four components. Our method is not intended for providing accurate diagnosis of the detected abnormal regions as esophageal cancer, but is intended to provide additional information to help doctors in their diagnosis. Therefore, our method only needs to detect all of the regions suspected of being cancer even if the detect results are false positives. We describe the procedure used in our method in detail and present experimental results demonstrating that our method is able to detect abnormal regions suspected of being early esophageal cancer using practical endoscopic images.

Indices for image quality degradation evaluation based on wavelet transforms

We present new indices for measuring the degradation of a digital image. Objective measures for assessing image quality, such as PSNR and SSIM, have been developed to quantify the visibility of errors or structural information between the original image and its modified version. However, the results obtained by PSNR and SSIM do not always match a subjective evaluation. We developed new indices based on the continuous wavelet transform (CWT) for measuring degradation so as to match a subjective evaluation. We also developed some indices based on the discrete wavelet transform (DWT) and investigated the usefulness of the proposed indices by conducting experiments.

Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations

Abstract We consider a numerical method to verify the existence and uniqueness of the solutions of nonlinear hyperbolic problems with guaranteed error bounds. Using a C 1 finite element solution and an inequality constituting a bound on the norm of the inverse operator of the linearized operator, we numerically construct a set of functions which satisfy the hypothesis of Banachs fixed point theorem for a continuous map on L p -space in a computer. We present detailed verification procedures and give some numerical examples.