Piecewise Rational Quadratic Interpolation to Monotonic Data

Gregory, John; Delbourgo, Roger

doi:10.1093/imanum/2.2.123

Cited by 145 publications

(80 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Alternatively, the endpoints of the image's tonal range may be remapped to set its white point and its black point. To ensure a continuously differentiable monotonic transformation for any valid choice of inputs, we rely on a piecewise rational quadratic interpolating spline [16,17]: As future research, it would be interesting to explore more precise control over where the histogram is stretched and compressed by using a piecewise rational cubic interpolating spline with adjustable shape parameters [17].…”

Section: Methodsmentioning

confidence: 99%

Interactive Contrast Enhancement by Histogram Warping

Grundland¹,

Dodgson²

2006

Computational Imaging and Vision

View full text Add to dashboard Cite

Abstract:We present an interactive contrast enhancement technique for the global histogram modification of images. Through direct manipulation, the user adjusts contrast by clicking on the image. Contrast around different key tones can be adjusted simultaneously and independently without altering their luminance. Histogram warping by monotonic splines performs the gray level mapping. User interfaces for contrast correction find application in digital photography, remote sensing, medical imaging, and scientific visualization.

show abstract

Section: Methodsmentioning

confidence: 99%

Interactive Contrast Enhancement by Histogram Warping

Grundland¹,

Dodgson²

2006

Computational Imaging and Vision

View full text Add to dashboard Cite

show abstract

“…In effect, a continuously differentiable transformation refrains from introducing artificial discontinuities into the resulting color density. To satisfy these requirements, our histogram warping transformation relies on a piecewise rational quadratic interpolating spline 41,42 :…”

Section: Color Transformationmentioning

confidence: 99%

Color histogram specification by histogram warping

Grundland

Dodgson

2005

SPIE Proceedings

View full text Add to dashboard Cite

Histogram warping is a novel histogram specification technique for use in color image processing. As a general purpose tool for color correction, our technique constructs a global color mapping function in order to transform the colors of a source image to match a target color distribution to any desired degree of accuracy. To reduce the risk of color distortion, the transformation takes place in an image dependent color space, featuring perceptually uniform color axes with statistically independent chromatic components. Eliminating the coherence between the color axes enables the transformation to operate independently on each color axis. Deforming the source color distribution to reproduce the dominant color features of the target distribution, the histogram warping process is controlled by designating the color shifts and contrast adjustments for a set of key colors. Assisted by mode detection, matching quantiles establish the correspondence between the color distributions. Interpolation by monotonic splines serves to extend the mapping over the entire dynamic range without introducing artificial discontinuities into the resulting color density. We show how our method can be applied to color histogram equalization as well as color transfer from an example image or a color palette.

show abstract

“…In Gregory and Delbourgo (1982) a C 1 monotonic interpolation method is described which interpolates given monotonic data. The purpose of this note is to develop explicit formulae for determining the derivative parameters of the scheme from the given function valued data.…”

Section: Introductionmentioning

confidence: 99%

“…

AbstractExplicit formulae are developed for determining the derivative parameters of a monotonic interpolation method of Gregory and Delbourgo (1982).

…”

mentioning

confidence: 99%