Ideal Histogram Research Articles

Equivalence of histogram equalization, histogram matching and the Nyul algorithm for intensity standardization in MRI

Intensity standardization is an important preprocessing step in automatedanalysis of MRI. A popular method by Nyul et al. uses apiece-wise linear approximation of histogram matching. We showthat this method is a non-uniform trapezoidal Riemann approximationof the ideal histogram matching operation, and suggest thathistogram matching is no better than histogram equalization for intensitystandardization in MRI. Experimental results are derived usingsynthetic data.

Gradient-norm-based histogram equalization taking account of HSV color space distribution

In the present paper, we propose an image contrast enhancement method that can enhance the contrast of a color image naturally by taking account of a color space shape. The proposed method realizes the natural enhancement based on two kinds of intensity histograms: a gradient-norm-based histogram and an ideal histogram derived from the shape of a color space. The former histogram is used to suppress over-enhancement in the flat regions of an image and the latter histogram is used to prevent the whole image from being darken. Concretely, the aforementioned intensity histograms are appropriately mixed into a histogram with a weight based on the average intensity of the input image. The contrast enhancement of the input image is realized using the cumulative histogram of the mixed histogram as an intensity transform function. To verify the validity of the proposed method, in experiments, the proposed method is applied to a variety of images and experimental results are evaluated qualitatively and quantitatively.

Multidimensional Histograms for Density Modification

Publisher Summary Density modification improves the quality of an approximate electron-density map by imposing physical constraints based on some conserved features of the correct electron density map. Density modification methods generally require an initial map with substantial phase information. In most cases, these phases are obtained from multiple isomorphous replacement (MIR) or multiwavelength anomalous dispersion (MAD), and these phases are of pivotal importance when the experimental source of phase information is bimodal as it is in single-wavelength anomalous scattering (SAD) and single isomorphous replacement methods (SIR). The most commonly used density modification method is solvent flattening that exploits the observation that the solvent region of an electron density map is featureless at medium resolution because of the high thermal motion and disorder of the solvent molecules. Xiang and Carter proposed extending the density histogram to include relationships between neighboring density values via multidimensional histograms defined as joint probabilities of the density values and their higher-order derivatives. In the conventional one-dimensional (1D) electron density histogram matching method, a one-to-one mapping is made on the original electron density to the new electron density so that the density histogram of the modified map matches that of the ideal histogram. The two-dimensional (2D) histogram specifies not only the probability of the electron density value for a given grid point in the map but also the local environment around that grid point as reflected by the density gradients that arise from chemical bonding. The strategy of using alternating 1D histogram matching to achieve 2D histogram matching can be generalized to the matching of higher dimension histograms.

Density histograms in protein electron crystallography—direct phase determination of bacteriorhodopsin at 6 Å resolution

Direct methods for crystallographic phase determination have been used to solve the projected structure of native glucose-embedded bacteriorhodopsin (plane group p3, a=62.4 Å) to 6 Å, without accepting any information from electron micrographs. After defining the origin and enantiomorph and adding one algebraic phase term to the basis set, expansions into the complete set of 50 unique reflections via the Sayre equation, testing four possible values of the algebraic term, could be screened with figures of merit based on the protein density histogram, where the auto-correlation function of the ideal histogram is an endpoint for the cross-correlation of experimental histogram with this ideal distribution. Initial phase determination, followed by Fourier refinement and some additional phase permutation, yields a solution with an overall mean phase error of 60.8 or 35.4° for the 18 most intense reflections.

Optimizing Sinusoidal Histogram Test for Low Cost ADC BIST

The histogram method is a very classical test technique for Analog to Digital Converters (ADCs), but only used for external testing because of the large amount of required hardware resources. This paper discusses the viability of a BIST implementation for this technique. An original approach is developed that permits to extract the ADC parameters with a reduced area overhead. This approach involves (i) the calculation of the parameters using approximations and (ii) the decomposition of the global test in a code-after-code test procedure. These two features allow a significant reduction of the required operative resources and memory dedicated to the storage of experimental data. In addition, the use of a piece-wise approximation for computing the ideal histogram also permits to minimize the memory dedicated to the storage of reference data.

High resolution method for the analysis of DNA histograms that is suitable for the detection of multiple aneuploid G1 peaks in clinical samples.

The DNA histogram obtained by flow cytometry can be considered as the product of an "ideal" measurement column vector and a measurement distortion matrix. In order to extract the ideal histogram from the real data, the measurement distortion matrix is commonly presumed to be a family of Gaussian coefficients that are centered on the diagonal. We have designed a feedback-controlled curve-fitting procedure that reconstructs the ideal histogram from the real data through successive iterations. The optimum coefficient of variation (cv) for the family of Gaussians in the measurement distortion matrix is determined from an analysis of the sums of squares of fits of the computed DNA histogram to the real data over an appropriate range of trial cv. Since this method assigns a Gaussian to each and every data channel, it permits the resolution of closely spaced multiple aneuploid G1 peaks in clinical samples. The effects of high frequency noise that may be present in the data can be attenuated by multiplying the real data histogram by a Gaussian matrix with cv close to but smaller than that of the measurement distortion matrix.