Histogram

Histogram

Statistical Representation of Images

This component calculates the statistical distribution of any given input image. Depending on the selected operating mode, this component can generate and display two different statistical representations:

1. Histogram ( $h$ ):

   Displays the frequency of pixel ( $\iota$ ) values across the image ( ${\rm I}$ ). This reveals how intensities are distributed, providing insight into contrast, brightness, and tonal balance.

   $h_i=\sum _{\iota \notin {\rm I}}\left[{\rm I}\right(\iota )=i]$

   
   

   Normalized:

   $h_i=\frac{1}{N}\sum _{\iota \notin {\rm I}}\left[{\rm I}\right(\iota )=i]$

   
   

2. Cumulative Distribution Function (CDF) ( $H$ ):

   Shows the running sum of those frequencies, mapping the cumulative proportion of pixels ( $\iota$ ) up to each value. The CDF ( $H$ ) is especially useful for tasks like histogram equalization, where pixel ( $\iota$ ) intensities are remapped to enhance contrast.

   $H_i=\sum _{j=0}^i{h}_j$

   
   

   Normalized:

   $H_i=\frac{1}{N}\sum _{j=0}^i{h}_j$

   
   

Within this component family, the Histogram COMP serves as the entry point: it generates and encodes these statistical representations so they can be interpreted by other Histogram operators in the workflow. By coupling the original image with its histogram or CDF, this component provides a streamlined way to analyze and share image statistics across TouchDesigner TOP networks.

Resources:

Download the .tox files
Image Histogram on Wikipedia
CDF on Wikipedia

Histogram Compilers

Metadata Extraction & Reconstruction

These two components manage the encoded metadata strip used by the Histogram component family. By design, the histogram or CDF data is appended to the bottom of the input image so it can travel through the TOP stream alongside the original texture. The deCompiler and reCompiler provide tools for explicitly separating or reconstructing this combined representation.

• Histogram deCompiler:

  Accepts a TOP input that contains both the image and its statistical metadata strip. Outputs two TOPs: the original image with the strip removed, and the extracted metadata on its own.




• Histogram reCompiler:

  Performs the reverse operation. Accepts two TOP inputs — an image and a histogram/CDF metadata strip — and appends them together into a single TOP. The result can then be read and used by other Histogram components.

Together, these operators make it possible to isolate, reuse, or restructure histogram metadata within a TouchDesigner workflow, providing flexibility for both analysis and creative manipulation.

Resources:

Download the .tox files
Image Histogram on Wikipedia
CDF on Wikipedia

Histogram Conversion

Statistical Representation Converter

This component processes an image with appended statistical metadata and converts the embedded representation between the two available modes:

1. Histogram ( $h$ ):

   Displays the frequency of pixel ( $\iota$ ) values across the image ( ${\rm I}$ ). This reveals how intensities are distributed, providing insight into contrast, brightness, and tonal balance.

   $h_i=\sum _{\iota \notin {\rm I}}\left[{\rm I}\right(\iota )=i]$

   
   

2. Cumulative Distribution Function (CDF) ( $H$ ):

   Shows the running sum of those frequencies, mapping the cumulative proportion of pixels ( $\iota$ ) up to each value. The CDF ( $H$ ) is especially useful for tasks like histogram equalization, where pixel ( $\iota$ ) intensities are remapped to enhance contrast.

   $H_i=\sum _{j=0}^i{h}_j$

   
   

In addition to format conversion, this component also provides an option to normalize the metadata so that values sum to 1, ensuring consistency across different inputs and improving comparability between images.

By maintaining both the image and its updated statistical strip together, the Histogram Conversion component allows for seamless switching between representations while preserving compatibility with other operators in the Histogram component family.

Resources:

Download the .tox files
Image Histogram on Wikipedia
CDF on Wikipedia

Histogram Equalization

Intensity Remapping

This component redistributes the pixel ( $\iota$ ) intensities of an image ( ${\rm I}$ ) to achieve a more uniform distribution of values, thereby enhancing contrast and making features more visible. Histogram Equalization works by mapping the original pixel ( $\iota$ ) values to new values according to the normalized Cumulative Distribution Function ( $H$ ).

Formally, the transformation function is defined as:

${\rm I}\text{'}\left(\iota \right)=(L-1)·H\left({\rm I}\right(\iota \left)\right)$

This mapping ensures that the output image’s histogram spans the available intensity range more evenly, improving contrast in areas that were previously compressed.

In practice, Histogram Equalization is especially useful for:

• Enhancing low‐contrast images (e.g., foggy or underexposed).

• Highlighting features in medical, scientific, or technical imagery.

• Preprocessing steps for segmentation or edge detection, where uniform contrast improves results.

Resources:

Download the .tox files
Histogram Equalization on Wikipedia
Histogram Equalization on Medium

Histogram Similarity

Statistical Difference Measurement

This component compares the statistical distributions of two images and calculates their difference as a single vector of distances, with one value for each channel (R, G, B, & A). Both inputs must contain appended statistical metadata; if the data is stored as CDFs, the component automatically converts them into Histograms before comparison.

The resulting distance vector quantifies how dissimilar the two distributions are, providing a detailed breakdown of per‐channel differences. A variety of comparison methods are provided, grouped into categories according to their mathematical basis:

1. Distance:

   Manhattan ( $L_1$ ):

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sum _i|p_i-q_i|$

   
   

   Euclidean ( $L_2$ ):

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sqrt{\sum _i{(p_i-q_i)}^2}$

   
   

   Chebyshev ( $L_{\infty }$ ):

   ${{\rm I}}_{\mathrm{(p,\; q)}}=max\left(\right|p_i-q_i\left|\right)$

   
   

   Fractional ( $0<r<1$ ):

   ${{\rm I}}_{\mathrm{(p,\; q)}}={\left(\sum _i{|p_i-q_i|}^r\right)}^{\frac{1}{r}}$

   
   



2. Correlation‐Based:

   Cosine Similarity:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=1-\frac{\sum _i{p}_i{q}_i}{\sqrt{\sum _i{p_i}^2}\sqrt{\sum _i{q_i}^2}}$

   
   

   Pearson’s Correlation Coefficient:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=1-\frac{\sum _i(p_i-\overline{p})(q_i-\overline{q})}{\sqrt{\sum _i{(p_i-\overline{p})}^2}\sqrt{\sum _i{(q_i-\overline{q})}^2}}$

   
   



3. Probability & Divergence:

   Hellinger Distance:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\frac{1}{\sqrt{2}}\sqrt{\sum _i{(\sqrt{p_i}-\sqrt{q_i})}^2}$

   
   

   Kolmogorov‐Smirnov Divergence:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=max\left(\right|P\left(i\right)-Q\left(i\right)\left|\right)$

   
   

   Cramér‐von Mises Criterion:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sum _i{\left(P\right(i)-Q(i\left)\right)}^2$

   
   

   Bhattacharyya Distance:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=-ln\left(\sum _i\sqrt{p_i{q}_i}\right)$

   
   

   Kullback‐Leibler Divergence (KL):

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sum _i{p}_{i}ln\left(\frac{p_i}{q_i}\right)$

   
   

   Jeffrey Divergence:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sum _i(p_i-q_i)ln\left(\frac{p_i}{q_i}\right)$

   
   



4. Intersection & Overlap:

   Histogram Intersection:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sum _{i}min(p_i,q_i)$

   
   

   Jaccard Index:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=1-\frac{\sum _{i}min(p_i,q_i)}{\sum _{i}max(p_i,q_i)}$

   
   



5. Composite & Weighted:

   Canberra 1:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sum _i\frac{|p_i-q_i|}{min\left(\right|p_i|,|q_i\left|\right)}$

   
   

   Canberra 2 (symmetric variant):

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sum _i\frac{|p_i-q_i|}{\left|p_i\right|+\left|q_i\right|}$

   
   

   Chi‐Square (${\chi }^2$ Statistic):

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sum _i\frac{{(p_i-q_i)}^2}{p_i+q_i}$

   
   

   Squared Chord:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sum _i{(\sqrt{p_i}-\sqrt{q_i})}^2$

   
   



6. Other:

   Bray‐Curtis Dissimilarity, Sørensen‐Dice Coefficient:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\frac{\sum _i|p_i-q_i|}{\sum _i(p_i+q_i)}$

   
   

   Matching Distance:

   ${{\rm I}}_{\mathrm{(p,\; q)}}=\sum _i|p_i-q_i|$

   
   

Unlike other operators in this Histogram component family that output TOPs, this component outputs a CHOP, containing the per‐channel distance values. This makes it a powerful tool for image similarity measurement, pattern recognition, and statistical analysis.

Resources:

Download the .tox files
Histogram Similarity Assessment