# Pixel-wise Orthogonal Decomposition for Color Illumination Invariant and Shadow-free Image

arXiv: https://arxiv.org/abs/1407.0010 · HTML: https://mlsanity.com/paper/1407.0010/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2014.

## Built on by (most cited first, 1 of 1)

- [Discrete Diffusion Bridges for Spatiotemporally Aligned Image Translation and Generation](https://mlsanity.com/paper/2608.29997/) (2026)

## Abstract (arXiv)

In this paper, we propose a novel, effective and fast method to obtain a color illumination invariant and shadow-free image from a single outdoor image. Different from state-of-the-art methods for shadow-free image that either need shadow detection or statistical learning, we set up a linear equation set for each pixel value vector based on physically-based shadow invariants, deduce a pixel-wise orthogonal decomposition for its solutions, and then get an illumination invariant vector for each pixel value vector on an image. The illumination invariant vector is the unique particular solution of the linear equation set, which is orthogonal to its free solutions. With this illumination invariant vector and Lab color space, we propose an algorithm to generate a shadow-free image which well preserves the texture and color information of the original image. A series of experiments on a diverse set of outdoor images and the comparisons with the state-of-the-art methods validate our method.