Department of Information Technology
Research lab
Modeling the Mixing Behavior of Colorants

Goals of the project

Collect spectral measurement data of the subtractive color mixings. Find and analyze methods for implementing automatic color mixing system. Project is a part of color research project in Department of Information Technology, Lappeenranta University of Technology.

Status of the project

Project started
Project is started by student Joni Kamarainen and his supervisor prof. Jussi Parkkinen
Measurements ready
Measurements ready. Results are measured by Minolta spectrophotometer and oil-based paints used as colorants. Colorant concentration in the mixture is measured by weighting machine.
Modeling based on basic regression analysis
Just a basic regression analysis in two or more dimensions for mixes. Exponential and polynomial regression results are not very good.
Modeling based on subtractive color mixing theory
Tested widely used Kubelka-Munk method, which gives pretty poor approximations for mixings.
Modeling based on neural networks (MLP)
Problem is compressed into three or four dimensions and MLP gives good results.
Experimental formula for colorant mixing
This formula is derived from the three dimensional representation of measurements. Approximation is very reasonable.
Testing formula for pigment data: Project 1
Matlab demonstration code ready.


No news is bad news!


Project initial report (finnish) (html) (ps 172k)

Project final report (finnish) (gzip ps 202k)
Väriaineiden sekoittumisen mallinnuksen loppuraportti. Sisältää teoriaa väriaineista, reflektanssista, värikoordinaatistoista, MLP-neuroverkosta, regressioanalyysistä ja uusista menetelmistä halutun värin tuottamiseen väriaineiden sekoituksena. Dokumentin avainsanoja ovat: väriaine, Kubelka-Munk, MLP, neuroverkko, väri, sekoittuminen.

Summary of project final raport(english) (html) (gzip ps 207k)
Not so final because project continues.

Project 1 report(finnish) (html) (gzip ps 68k)
Testing colorant mixture formula for pigment measurements(only finnish).


Colorant mixing formula (html) (gzip ps 200k)

Colorant mixing test report (html) (ps 227k)
Mixing formula applied to two types of measurement data. You can also check demo (zip file) for matlab. Colorant mixing formula functionality and 7 demos included. Download and read README and check also Contents.m file.


Spectral data from the color mixings. All measures are easily transferable to Matlab. First column contains the ratio of substrate color in mix, so that it is 1 when pure substrate and 0 if there is no substrate at all. First row is allways pure substrate (white,yellow...) and last row is allways pure colorant. One dataset is allways a one whole measurement when substrate is transferred to some other color by adding that colorant step by step. All spectral data is reflectance values from 400nm to 700nm by 10nm (vector size 31). Example picture.
Mix 1. used colors (ascii)
Mix 1.1(ascii)
Mix 1.4(ascii)
Mix 1.5(ascii)
Mix 1.6(ascii)
Mix 1.7(ascii)
Mix 1.8(ascii)
Mix 1.9(ascii)
Mix 1.10(ascii) First row is pure white, then two times added red colorant and after that three times green colorant and last once again red colorant.
Mix 1.11(ascii) First row pure white colorant (substrate), then two times added blue colorant and then two times added red colorant.
All measuring data in three dimension(ascii) points (x,y,z) are x: coefficient of reflectances, y: concentration and z: factor for mixing of these colors.
Project 1 sources, measurements and docs Matlab sourcecodes, documents etc for project 1, what was for testing and developing colorant mixture formula for gray pigment measurements. (to uncompress (in unix), type first 'gunzip project1.tar.gz' and then 'tar xfv project1.tar').
Here is also zip-file for windows (uncompress with winzip etc.).

Links to other resources

Annotated Machine Vision Bibliography: Table of Contents
Color Conversion Algorithms
Color research - Lappeenranta University of Technology
Color theory page
Colour Science Glossary
The Beer's Law Controversy: Is it Linear for Dark Beers?

Chronological bibliography of this color science area

DELF, Thomas. c. 1855. The principles of colouring in painting (London: Winson & Newton).
ABNEY, William de Wiveleslie. 1891. Colour measurement and mixture (London: Society for Promoting Christian Knowledge).
ROOD, Roland. 1941. Color and light in painting (New York: Columbia University Press).
HILER, Hilaire. 1942. Color harmony and pigments (Chicago).
LEKSEYEV, S. S. 1962. On color and paints (Isskustvo).
BIRREN, Faber. 1965. History of color in painting, with new principles of color expression (New York: Van Nostrand Reinhold).
VOLKOV, N. N. 1965. Color in paintry (Isskustvo).
YULE, J. A. C. 1967. Principles of color reproduction applied to photo-mechanical reproduction, color photography and the ink, paper and other related industries (New York: John Wiley & Sons).
SBORNE, Roy. 1980. Lights and pigments, colour principles for artists (London: John Murray).
McLAREN, Keith. 1983. The colour science of dyes and pigments (Bristol, England: Adam Hilger). 2nd ed. 1986.
SHASHLOV, B. A. 1986. Color and its reproduction (Kniga).
ZOLLINGER, Heinrich. 1987. Color chemistry (New York: VCH Publishers).
HUNT, R. W. G. 1988. The reproduction of colour in photography, printing and television (Tolworth, England: Fountain Press).
VACHON, Guy. 1988. Modeling the Mixing Behavior of Inks with Polynomials, Color research and application, vol 13 nr 1 feb 1988

Contact information

prof. Jussi ParkkinenE-mail WWW
student Joni KämäräinenE-mail WWW

Last changes: $Date: 1999/05/04 00:33:23 $ by $Author: jkamarai $