Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

Application of the principle of dyadic symmetry to the generation of orthogonal transforms

Abstract: Two new transforms which can be used as substitutes for the Walsh transform are generated using the theory of dyadic symmetry. The new transforms have virtually the same complexity and computational requirements as the Walsh transform, employing additions, subtractions and binary shifts only, but have an efficiency, defined in terms of their ability to decorrelate signal data, which lies between that of the Walsh transform and that of the discrete cosine transform.

The Schrödinger distance transform (SDT) for point-sets and curves

Abstract: Despite the ubiquitous use of distance transforms in the shape analysis literature and the popularity of fast marching and fast sweeping methods — essentially Hamilton-Jacobi solvers, there is very little recent work leveraging the Hamilton-Jacobi to Schrodinger connection for representational and computational purposes. In this work, we exploit the linearity of the Schrodinger equation to (i) design fast discrete convolution methods using the FFT to compute the distance transform, (ii) derive the histogram of oriented gradients (HOG) via the squared magnitude of the Fourier transform of the wave function, (iii) extend the Schrodinger formalism to cover the case of curves parametrized as line segments as opposed to point-sets, (iv) demonstrate that the Schrodinger formalism permits the addition of wave functions — an operation that is not allowed for distance transforms, and finally (v) construct a fundamentally new Schrodinger equation and show that it can represent both the distance transform and its gradient density — not possible in earlier efforts.

Comprehensive Performance Comparison of Cosine, Walsh, Haar, Kekre, Sine, Slant and Hartley Transforms for CBIR with Fractional Coefficients of Transformed Image

Abstract: The desire of better and faster retrieval techniques has always fuelled to the research in content based image retrieval (CBIR). The extended comparison of innovative content based image retrieval (CBIR) techniques based on feature vectors as fractional coefficients of transformed images using various orthogonal transforms is presented in the paper. Here the fairly large numbers of popular transforms are considered along with newly introduced transform. The used transforms are Discrete Cosine, Walsh, Haar, Kekre, Discrete Sine, Slant and Discrete Hartley transforms. The benefit of energy compaction of transforms in higher coefficients is taken to reduce the feature vector size per image by taking fractional coefficients of transformed image. Smaller feature vector size results in less time for comparison of feature vectors resulting in faster retrieval of images. The feature vectors are extracted in fourteen different ways from the transformed image, with the first being all the coefficients of transformed image considered and then fourteen reduced coefficients sets are considered as feature vectors (as 50%, 25%, 12.5%, 6.25%, 3.125%, 1.5625% ,0.7813%, 0.39%, 0.195%, 0.097%, 0.048%, 0.024%, 0.012% and 0.06% of complete transformed image coefficients). To extract Gray and RGB feature sets the seven image transforms are applied on gray image equivalents and the color components of images. Then these fourteen reduced coefficients sets for gray as well as RGB feature vectors are used instead of using all coefficients of transformed images as feature vector for image retrieval, resulting into better performance and lower computations. The Wang image database of 1000 images spread across 11 categories is used to test the performance of proposed CBIR techniques. 55 queries (5 per category) are fired on the database o find net average precision and recall values for all feature sets per transform for each proposed CBIR technique. The results have shown performance improvement (higher precision and recall values) with fractional coefficients compared to complete transform of image at reduced computations resulting in faster retrieval. Finally Kekre transform surpasses all other discussed transforms in performance with highest precision and recall values for fractional coefficients (6.25% and 3.125% of all coefficients) and computation are lowered by 94.08% as compared to Cosine or Sine or Hartlay transforms.

Fast computation of the two-dimensional generalised Hartley transforms

Abstract: The two-dimensional generalised Hartley transforms (2-D GDHTs) are various half-sample generalised DHTs, and are used for computing the 2-D DHT and 2-D convolutions Fast computation of 2-D GDHTs is achieved by solving (n1+(n01/2))k1+(n2+(n02/2))k2=(n+( 1/2 ))k mod N, n01, n02=1 or 0 The kernel indexes on the left-hand side and on the right-hand side belong to the 2-D GDHTs and the 1-D H3, respectively This equation categorises N*N-point input into N groups which are the inputs of a 1-D N-point H3 By decomposing to 2-D GDHTs, an N*N-point DHT requires a 3N/2i 1-D N/2i-point H3, i=1, , log2N-2 Thus, it has not only the same number of multiplications as that of the discrete Radon transform (DRT) and linear congruence, but also has fewer additions than the DRT The distinct H3 transforms are independent, and hence parallel computation is feasible The mapping is very regular, and can be extended to an n-dimensional GDHT or GDFT easily

Envelope detection using generalized analytic signal in 2D QLCT domains

Abstract: The hypercomplex 2D analytic signal has been proposed by several authors with applications in color image processing. The analytic signal enables to extract local features from images. It has the fundamental property of splitting the identity, meaning that it separates qualitative and quantitative information of an image in form of the local phase and the local amplitude. The extension of analytic signal of linear canonical transform domain from 1D to 2D, covering also intrinsic 2D structures, has been proposed. We use this improved concept on envelope detector. The quaternion Fourier transform plays a vital role in the representation of multidimensional signals. The quaternion linear canonical transform (QLCT) is a well-known generalization of the quaternion Fourier transform. Some valuable properties of the two-sided QLCT are studied. Different approaches to the 2D quaternion Hilbert transforms are proposed that allow the calculation of the associated analytic signals, which can suppress the negative frequency components in the QLCT domains. As an application, examples of envelope detection demonstrate the effectiveness of our approach.