Optical Review

, Volume 26, Issue 6, pp 583–589 | Cite as

Direct and inverse converting between 4-band color space and HSI4: mathematical tool for multispectral image processing of 4 primary colors

  • Marco Antonio AlonsoEmail author
  • Antonio Benítez
  • Jacob Javier Vásquez
  • Mario Espinosa
  • José Javier Báez
Regular Paper


In this article, a new mathematical proposal is presented to perform digital multispectral images processing of four primary colors; namely, it shows the method and equations that transform the four-band color space (extension of RGB) into the space of color HSI4 (HSI color model that depends on four primary colors) and vice versa. The HSI model is widely used to develop image processing algorithms based on human perception of color. At present, there are capture and visualization devices based on four primary colors that is why the information contained in this document will be a valuable mathematical tool in the processing of images in the HSI space. The work is divided into two main parts: direct converting, which is based on an already developed article and what is presented here is an application of this one for the case of four primary colors. The second part, inverse converting, is the most important and new contribution. The effectiveness of the mathematical proposal can be verified with the numerical results presented.


HSI and RGB color models Multispectral image Primary colors Converting colors Vector analytic geometry 


Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© The Optical Society of Japan 2019

Authors and Affiliations

  1. 1.Postgraduate DepartmentUniversidad Politécnica de PueblaPueblaMexico
  2. 2.Department of OpticsInstituto Nacional de AstrofísicaPueblaMexico

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