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.
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.
Details
- HistogramTransformInterpolation returns a function to perform a histogram transformation by changing the shape of the image histogram, typically used for histogram equalization or matching.
- HistogramTransformInterpolation returns a function f or a list of functions for each channel, each represented with an InterpolatingFunction .
- Use HistogramTransform to perform histogram transformation using the corresponding functions.
- HistogramTransformInterpolation [image] is effectively the cumulative distribution (CDF) of the pixel values. When applied to pixel values, it creates an image with a nearly flat histogram.
- HistogramTransformInterpolation [image,ref] finds a function such that the transformed pixel values would have nearly the same distribution as ref.
- Reference ref can be another image, a dataset or a distribution.
- HistogramTransformInterpolation works with 2D and 3D images, and also with lists of arbitrary rank datasets.
- HistogramTransformInterpolation [{data1,data2,…},…] gives a list of functions that correspond to each dataset.
- With HistogramTransformInterpolation [image,ref], 256 quantiles are used.
- With HistogramTransformInterpolation [data,ref,Automatic ], the number of quantiles is the same as the number of bins used in Histogram [data].
Examples
open all close allBasic 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)
Locally Adaptive Histogram Equalization (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:
Related Guides
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_2025_histogramtransforminterpolation, author="Wolfram Research", title="{HistogramTransformInterpolation}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/HistogramTransformInterpolation.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_histogramtransforminterpolation, organization={Wolfram Research}, title={HistogramTransformInterpolation}, year={2014}, url={https://reference.wolfram.com/language/ref/HistogramTransformInterpolation.html}, note=[Accessed: 17-November-2025]}