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Modeling the Diffusion of Chemical Contamination in Soil with Non-Conventional Differential Operators
Published in Abdon Atangana, Mathematical Analysis of Groundwater Flow Models, 2022
A fractal is a continuous pattern that repeats itself at various scales. Fractals are used to investigate anomalous systems occurring in nature. They are one of the latest developments in statistics and inhabit scaling and self-similar properties. Scaling is the ability of objects to increase or decrease in size by a scale factor that is the same in all dimensions. Self-similarity is the capacity of an object to duplicate itself. Fractal derivatives are of a self-similar nature and repeat themselves at various scales in space and time. Fractals are believed to have links to fractional derivatives, Levy statistics, Brownian motion, and empirical power-law scaling (Chen, 2005). The fractal derivative can be used describe motion in turbulence, fractal flow, and viscos-elastic behavior (Chen et al., 2017). Chen (2017) replaces the inter-order time derivative with a fractal derivative using the power law to describe the anomalous diffusion in heterogeneous media. The following equation gives the fractal derivative: ∂u∂tα=limt1→tut1−utt1α−tαα>0
Watermarking Attacks and Tools
Published in Frank Y. Shih, Digital Watermarking and Steganography: Fundamentals and Techniques, 2017
Image scaling can have two types: uniform and nonuniform scaling. Uniform scaling uses the same scaling factors in the horizontal and vertical directions. However, nonuniform scaling applies different scaling factors in the horizontal and vertical directions. In other words, the aspect ratio is changed in nonuniform scaling. An example of nonuniform scaling using x scale = 0.8 and y scale = 1 is shown in Figure 5.8. Note that nonuniform scaling will produce the effect of object shape distortion. Most digital watermarking methods are designed to be flexible only to uniform scaling.
Watermarking Attacks and Tools
Published in Frank Y. Shin, Digital Watermarking and Steganography, 2017
Image scaling can be of one of two types: uniform or nonuniform. Uniform scaling uses the same scaling factors in horizontal and vertical directions. However, nonuniform scaling applies different scaling factors in horizontal and vertical directions. In other words, the aspect ratio is changed in nonuniform scaling. An example of nonuniform scaling using xscale = 0.8 and yscale = 1 is shown in Figure 5.8. Note that the nonuniform scaling will produce the effect of object shape distortion. Most digital watermarking methods are designed to be flexible only to uniform scaling.
Gender and Age Classification Enabled Blockschain Security Mechanism for Assisting Mobile Application
Published in IETE Journal of Research, 2021
Sapna Juneja, Sourav Jain, Aparna Suneja, Gurminder Kaur, Yasser Alharbi, Ali Alferaidi, Abdullah Alharbi, Wattana Viriyasitavat, Gaurav Dhiman
It is helpful in applications involving the scaling of images. Scaling refers to resizing of an image. Scale-up means making the image size bigger whereas Scale down makes the image smaller. SIFT is also used to detect corners, circles, blobs, etc. The following procedure is followed by this algorithm. Scale Space Extrema Detection – It involves the blurring the image and then resizing the original image to half. Also, blur the resized image. Blurring is nothing but a convolution of the Gaussian operator and image. By doing so, we create a Scale Space. The difference of Gaussian (DOG) [25] is calculated. DOG images are equivalent to the Laplace of Gaussian image.Finding Key points – Once the image is blurred using DOG, the pixel is compared with eight neighbours and also with nine pixels in the next and previous scales. If that pixel is the least or greatest, then it means it is either maxima or minima, or we can simply say it is local extrema. Local extrema are also called potential key point. After that sub pixel maxima/minima is found out. Sub pixel values are generated using Taylor expansion of image around the found key point.Key point Localisation – All bad key points like edges, low contrast features (whose intensity at a current pixel is less than the threshold value) are eliminated.Orientation Assignment – Orientations are assigned to each key point. For every orientation, a histogram is created. Peak above 80% or the highest peak of the histogram is considered.Key point Descriptor and Key point Matching – Descriptors are the vectors that have a size of (number of key points obtained from previous stages) * 128. Key point Matching is done between two images by identifying nearest neighbours. Then ratio analysis is done between the closest and second closest. One of the main drawbacks of this algorithm is the high dimensionality of a descriptor. If we try to reduce the dimensions, the cost increases gradually.