# HistogramTransformInterpolation

HistogramTransformInterpolation[{x1,x2,}]

finds a function so that the transformed values are distributed nearly uniformly.

HistogramTransformInterpolation[{x1,x2,},ref]

finds so that are distributed with distribution ref.

HistogramTransformInterpolation[{x1,x2,},ref,n]

finds a function with n equally spaced quantiles.

HistogramTransformInterpolation[image,]

finds a function that reshapes the histogram of image.

# Examples

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## Basic Examples(4)

Find a function that distributes samples in a given dataset uniformly:

Reshape the histogram of a dataset to match the PDF of a normal distribution:

Find a function that equalizes the histogram of an image:

Find a function that equalizes the histogram of a 3D image:

## Scope(3)

Find equalizing functions for a list of datasets:

Find histogram reshaping functions for each color channel:

Apply the functions channel by channel:

Use a different number of quantiles when finding the transformation function:

## Applications(1)

A full locally adaptive histogram equalization may give more appealing results for images with a variety of intensity levels, but takes much more time:

Bilinear interpolation between the equalization functions computed for non-overlapping blocks is a faster approximation:

## Properties & Relations(2)

HistogramTransformInterpolation can be used to get the transformation function used in HistogramTransform:

The result of HistogramTransformInterpolation approximates the closed-form solution when it exists:

Wolfram Research (2012), HistogramTransformInterpolation, Wolfram Language function, https://reference.wolfram.com/language/ref/HistogramTransformInterpolation.html (updated 2014).

#### Text

Wolfram Research (2012), HistogramTransformInterpolation, Wolfram Language function, https://reference.wolfram.com/language/ref/HistogramTransformInterpolation.html (updated 2014).

#### CMS

Wolfram Language. 2012. "HistogramTransformInterpolation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/HistogramTransformInterpolation.html.

#### APA

Wolfram Language. (2012). HistogramTransformInterpolation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HistogramTransformInterpolation.html

#### BibTeX

@misc{reference.wolfram_2024_histogramtransforminterpolation, author="Wolfram Research", title="{HistogramTransformInterpolation}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/HistogramTransformInterpolation.html}", note=[Accessed: 07-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_histogramtransforminterpolation, organization={Wolfram Research}, title={HistogramTransformInterpolation}, year={2014}, url={https://reference.wolfram.com/language/ref/HistogramTransformInterpolation.html}, note=[Accessed: 07-August-2024 ]}