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Hermite-Based Deformable Models for Cardiac Image Segmentation
Published in Ayman El-Baz, Jasjit S. Suri, Cardiovascular Imaging and Image Analysis, 2018
Jimena Olveres, Erik Carbajal-Degante, Boris Escalante-Ramírez, Leiner Barba-J, Lorena Vargas-Quintero, Enrique Vallejo Venegas, Lisbeth Camargo Marín, Mario Guzmán Huerta
The Hermite transform is a special case of a polynomial transform that incorporates biological properties due to the similarity between Gaussian derivatives and receptive fields in the human visual system [49, 32, 33]. The main advantage of this tool is the easy extraction of important details as lines, edges, and texture information by applying a decomposition scheme.
Image encryption algorithm based on the fractional Hermite transform
Published in Journal of Modern Optics, 2021
Li-Hua Gong, Jing Zeng, Xiao-Zhen Li
The interference of various noises during the process of channel transmission may seriously affect the quality of decryption images [20]. Compared with the traditional Fourier transform, the Hermite transform has better image recognition ability and better noise tolerance [21]. The Hermite transform is a peculiar case of polynomial transform, whose core content is Hermite polynomial [22]. Because of its outstanding performance in noise reduction and image retrieval, Hermite transform has been widely employed in image processing [23]. In 2020, Shinde et al. devised a new flexible directional filter by adjusting the order of Hermite transform, which enhances the performance of the image retrieval system [24]. To make the image encryption system more robust to noise, Neto et al. constructed a number-theoretic transform based on generating matrix [25]. Joshi demonstrated how to construct the orthogonal basis of the eigenvector of Hermite-Gaussian-like with a special generating matrix [26]. The introduction of generating matrix not only promotes the image encryption scheme to be extended from time domain to frequency domain mathematically, but also helps better understand the fractional order transform, such as the discrete fractional Fourier transform (DFrFT) [27]. Similarly, the generating matrix was utilized to analyse the convergence of the feature vectors and the corresponding continuous Hermite-Gaussian function samples [28], so as to better understand the properties of the fractional Fourier transform [29]. The fractional Fourier transform has the characteristic of time–frequency rotation [30]. As the transform order increases from 0 to 1, the fractional Fourier transform shows all the characteristics of the signal from time domain to frequency domain [31]. In other words, the fractional Fourier transform can present the frequency plane of the function, which makes the correlation between the functions intuitive [32]. With the help of the properties of the fractional Fourier transform, the concept of fractional order can be applied to Hermite transform [33]. The input non-stationary signal can be better processed via the fractional Hermite transform (FHT), and the angle with the most concentrated information in the signal can be reasonably selected. The FHT could be regarded as a signal decomposition technique and is a convolution process of an input function and a window function as an analysis filter [34]. This window function can sample the input signal equally. To facilitate the analysis of important parts of the input signal, a weighting function was also deliberately introduced in the window function [35]. The optimal order of the FHT was achieved by selecting the result with the largest amplitude among different fractional orders. Through the centralized protection of the important information, the noise impacting on the input signal was minimized [36].