Gradient in spectral and color images: from the Di Zenzo initial construction to a generic proposition.

In this article, we define a generic gradient for color and spectral images, considering a proposed taxonomy of the state of the art. A full-vector gradient, taking into account the sensor's characteristics, is in compliance with the metrological properties of genericity, robustness, and reproducibility. Here, we construct a protocol to compare gradients from different sensors. The comparison is developed by simulating sensors using their spectral characteristics. We develop three experiments using this protocol. The first experiment shows the consistency of results for similar sensors; the second demonstrates the genericity of the approach, adapted to any kind of imaging sensors; and the third focuses on the channel inter-correlation considering sensors such as in the color vision deficiency case.

Full-Vector Gradient for Multi-spectral or Multivariate Images.

Gradient extraction is important for a lot of metrological applications such as Control Quality by Vision. In this work, we propose a full-vector gradient for multi-spectral sensors. The full-vector gradient extends Di Zenzo expression to take into account the non-orthogonality of the acquisition channels thanks to a Gram matrix. This expression is generic and independent from channel count. Results are provided for a color and a multi-spectral snapshot sensor. Then, we show the accuracy improvement of the gradient calculation by creating a dedicated objective test and from real images.