Lossless compression of Peanoscanned images

Provine, Joseph A.; Rangayyan, Rangaraj M.

doi:10.1117/12.171928

Cited by 14 publications

(6 citation statements)

References 19 publications

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“…The Hilbert curve [42] is one of the well-recognized fractals that demonstrates this behavior. An important property of the Hilbert curve, also referred to as the Peano curve or the Peano-Hilbert curve [51], is that it visits all of the subsquares or their center points in a given quadrant or subquadrant of the given space before leaving the same for the next subquadrant. In contrast to this notion of dimension, Hilbert demonstrated that a curve can fill a 2D plane, that is, after an infinite number of iterations, the Hilbert curve will pass through every point in a plane without crossing itself.…”

Section: Famous Fractalsmentioning

confidence: 99%

Fractal Analysis of Breast Masses in Mammograms

Cabral

Rangayyan

2012

Synthesis Lectures on Biomedical Engineering

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Lectures in Biomedical Engineering will be comprised of 75-to 150-page publications on advanced and state-of-the-art topics that span the field of biomedical engineering, from the atom and molecule to large diagnostic equipment. Each lecture covers, for that topic, the fundamental principles in a unified manner, develops underlying concepts needed for sequential material, and progresses to more advanced topics. Computer software and multimedia, when appropriate and available, are included for simulation, computation, visualization and design. The authors selected to write the lectures are leading experts on the subject who have extensive background in theory, application and design. The series is designed to meet the demands of the 21st century technology and the rapid advancements in the all-encompassing field of biomedical engineering that includes biochemical, ABSTRACTFractal analysis is useful in digital image processing for the characterization of shape roughness and gray-scale texture or complexity. Breast masses present shape and gray-scale characteristics in mammograms that vary between benign masses and malignant tumors. This book demonstrates the use of fractal analysis to classify breast masses as benign masses or malignant tumors based on the irregularity exhibited in their contours and the gray-scale variability exhibited in their mammographic images. A few different approaches are described to estimate the fractal dimension (FD) of the contour of a mass, including the ruler method, box-counting method, and the power spectral analysis (PSA) method. Procedures are also described for the estimation of the FD of the gray-scale image of a mass using the blanket method and the PSA method.To facilitate comparative analysis of FD as a feature for pattern classification of breast masses, several other shape features and texture measures are described in the book. The shape features described include compactness, spiculation index, fractional concavity, and Fourier factor.The texture measures described are statistical measures derived from the gray-level cooccurrence matrix of the given image. Texture measures reveal properties about the spatial distribution of the gray levels in the given image; therefore, the performance of texture measures may be dependent on the resolution of the image. For this reason, an analysis of the effect of spatial resolution or pixel size on texture measures in the classification of breast masses is presented in the book.The results demonstrated in the book indicate that fractal analysis is more suitable for characterization of the shape than the gray-level variations of breast masses, with area under the receiver operating characteristics of up to 0.93 with a dataset of 111 mammographic images of masses. The methods and results presented in the book are useful for computer-aided diagnosis of breast cancer.

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Section: Famous Fractalsmentioning

confidence: 99%

Fractal Analysis of Breast Masses in Mammograms

Cabral

Rangayyan

2012

Synthesis Lectures on Biomedical Engineering

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“…It is defined in the following way: (28) where is the mean-squared error between the luminance channel of the reconstructed and the original frames. In the case of TMN4, the PSNR frame distortion can be written as (29) since the region distortion only depends on the selected motion vector and the selected quantizer for that region. We use "quarter common intermediate format" (QCIF) sequences, which have dimensions 176 144 pixels.…”

Section: A Video Compression Scheme With Optimal Bit Allocation Bementioning

confidence: 99%

“…Hilbert curves have been used in image and video processing as scanning paths on the pixel level in the luminance domain for lossless coding [29] and lossy coding [30]. They have also been used as a scanning path for the coefficients in the transform domain [31].…”

Section: A Video Compression Scheme With Optimal Bit Allocation Bementioning

confidence: 99%

A theory for the optimal bit allocation between displacement vector field and displaced frame difference

Schuster

Katsaggelos

1997

IEEE J. Select. Areas Commun.

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In this paper, we address the fundamental problem of optimally splitting a video sequence into two sources of information, the displaced frame difference (DFD) and the displacement vector field (DVF). We first consider the case of a lossless motion-compensated video coder (MCVC), and derive a general dynamic programming (DP) formulation which results in an optimal tradeoff between the DVF and the DFD. We then consider the more important case of a lossy MCVC, and present an algorithm which solves the tradeoff between the rate and the distortion. This algorithm is based on the Lagrange multiplier method and the DP approach introduced for the lossless MCVC. We then present an H.263-based MCVC which uses the proposed optimal bit allocation, and compare its results to H.263. As expected, the proposed coder is superior in the rate-distortion sense. In addition to this, it offers many advantages for a rate control scheme. The presented theory can be applied to build new optimal coders, and to analyze the heuristics employed in existing coders. In fact, whenever one changes an existing coder, the proposed theory can be used to evaluate how the change affects its performance.

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“…For all images they investigated, Abdollahi et al achieved the lowest entropy-ratios when the Hilbert Curve was applied. Provine and Rangayyan compress greyscale images mapped with the Hilbert and Raster Curves using HFF, Arithmetic Coding, Predictive Coding, and LZW [35]. The highest compression ratios they achieve, of approximately R c = 5, are obtained with HFF combined with differential coding, a form of predictive coding.…”

Section: Introductionmentioning

confidence: 99%

Effect of d-Dimensional Re-orderings on Lossless Compression of Radio-Astronomy and Digital Elevation Data

2021

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For multidimensional data, Space-Filling Curves (SFCs) have been used to improve the execution time of spatial data queries. However, their effect on compression, when used to reorder the uncompressed values, is known to a lesser extent. We investigate the impact of three SFCs on Shuttle Radar Topographic Mission (SRTM) elevation data and Square-Kilometre Array telescope (SKA) radio-astronomy data: two types of datasets to which SFCs have not been extensively applied, within a compression context. This work contributes to the understanding of how such reorderings impact compression performance and affect different compression schemes and preprocessing techniques through their use. We show empirical results from combining eight common compression schemes, the Z-Order, Gray-Code, and Hilbert spacefilling curves, and the bitwise preprocessing technique BitShuffle. The Hilbert Curve consistently outperforms the other orderings for the SRTM dataset though the mapping implementation incurs a significant speed penalty. However, the Z-Order and Gray-Code Curves are best for the SKA dataset. Through an analysis of the dataset autocorrelations, file-entropies, and block-entropies; we show that the SKA dataset's dimensional bias is not exploited as much by the Hilbert Curve compared to the Z-Order and Gray-Code Curves. However, the Hilbert Curve is the most appropriate for the SRTM dataset as it can be modelled as isotropic and has a significantly higher level of local autocorrelation. BitShuffle is necessary to practically compress the SKA data, but does contribute to the compression performance of the SRTM dataset. These curves and BitShuffle are advantageous in reducing block-entropy values for such datasets.

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Lossless compression of Peanoscanned images

Cited by 14 publications

References 19 publications

Fractal Analysis of Breast Masses in Mammograms

Fractal Analysis of Breast Masses in Mammograms

A theory for the optimal bit allocation between displacement vector field and displaced frame difference

Effect of d-Dimensional Re-orderings on Lossless Compression of Radio-Astronomy and Digital Elevation Data

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