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Digital Image Representation
Published in Jiří Jan, Medical Image Processing, Reconstruction and Analysis, 2019
Still another real-valued transform related to two-dimensional DFT is the two-dimensional Hartley transform. Being separable, it can be defined by A¯¯R=A¯¯C=1N[ak,n]=1N[sin(2πknN)+cos(2πknN)]. In a sense, the Hartley transform is a compromise between the sine and the cosine transforms, its basis functions again being real harmonic functions, but phase shifted by ±π/4 with respect to the pure sine or cosine basis.
Separation of Machine-Printed and Handwritten Texts in Noisy Documents using Wavelet Transform
Published in IETE Technical Review, 2019
Generally, it is seen that handwritten text and noise are identified by one class. To tackle this issue, properties like texture smoothness and abrupt variations in intensity levels are exploited for these classes. Standard transforms like discrete Hartley transform [5] and discrete Fourier transform [6] extract detail information efficiently in one dimension. With reference to two-dimensional signal like an image, these transforms capture details if the two-dimensional signal is represented by a set of one-dimensional signal functions. Moreover, noise contains smooth variations in document images. These variations consist of distinguishable information that can be easily captured using discrete wavelet transform (DWT) at different resolution levels and in different directions. In addition, the features based on means and variances of a wavelet-decomposed image provide information related to energy distribution of sub-bands. Hence, these features characterize the textures more effectively [7]. Recent transforms like curvelets [8] and contourlets [9] also pose multi-directional properties and are proficient to approximate the smooth curves or variations of texts easily. However, these transforms are complicated in nature and computationally expensive. As a result, training and testing of big databases using these transforms become very slow. Herein the proposed algorithm, directionality of DWT is further enhanced by combining it with SDDWT.
Asymmetric encryption algorithm for colour images based on fractional Hartley transform
Published in Journal of Modern Optics, 2019
A. K. Yadav, Phool Singh, Indu Saini, Kehar Singh
The application of fractional Hartley transform (FRHT) (39–50) in image encryption is comparatively less explored. Zhao et al. (40) pointed out that FRHT does not satisfy the additive property, and therefore, the original image cannot be recovered as a result of decryption. They proposed a redefined fractional Hartley transform which uses fractional Fourier transform and has a period 2. In additional to FRHT’s mathematical definition, they also reported its optical implementation. Li and Zhao (41) proposed a method for colour image encryption by wavelength multiplexing. Vilardy et al. (43) have used the Arnold transform in the fractional Hartley domain for double-image encryption. Liu et al. (44) have reported an algorithm for single-channel colour image encryption based on vector operation and fractional Hartley transform. A few recent studies (47, 49–51) have reported image encryption schemes in the fractional Hartley domain using the Arnold transform and singular value decomposition, respectively, for amplitude (47, 50, 51) and phase images (49).
Asymmetric hybrid encryption scheme based on modified equal modulus decomposition in hybrid multi-resolution wavelet domain
Published in Journal of Modern Optics, 2019
Pankaj Rakheja, Rekha Vig, Phool Singh
The optical cryptosystems have gained a lot of popularity among researchers due to their inherent properties of large information capacity, parallel processing and high speed. Refregier and Javidi (1) proposed double random phase encoding (DPRE) in 1995. DPRE-based optical schemes were investigated and further enhanced by various researchers using different techniques: in fractional Fourier domain (2, 3), in Fresnel domain (4), using amplitude modulation (5), using fractional Fourier transform in digital holography (6), using diffractive imaging (7), using phase retrieval algorithm and intermodulation in Fourier domain (8). To improve the security of optical encryption schemes, various advanced technologies are combined in many ways such as image encoding based on multi-stage and multi-channel fractional Fourier transform (9), random binary phase modulation with mixture retrieval type of Yang-Gu algorithm (10), gyrator and Arnold transform (11), digital holography and joint correlators (12, 13), fractional Mellin transform (14), Hartley transform (15), Arnold transform and singular value decomposition in fractional Hartley domain (16), wavelet domain (17), gyrator wavelet transform (18), phase shifting interferometry (19), phase retrieval algorithm (20), photo counting and photo counting polarimetric image encryption (21, 22), compression-based image encryption (23, 24), diffraction imaging-based encryption and their vulnerability to ptychographic phase retrieval (25), encryption based on computational ghost imaging (26), encryption based on quantum imaging (27) and so on.