The Quantum Nature of Color Perception: Uncertainty Relations for Chromatic Opposition.

In this paper, we provide an overview on the foundation and first results of a very recent quantum theory of color perception, together with novel results about uncertainty relations for chromatic opposition. The major inspiration for this model is the 1974 remarkable work by H.L. Resnikoff, who had the idea to give up the analysis of the space of perceived colors through metameric classes of spectra in favor of the study of its algebraic properties. This strategy permitted to reveal the importance of hyperbolic geometry in colorimetry. Starting from these premises, we show how Resnikoff's construction can be extended to a geometrically rich quantum framework, where the concepts of achromatic color, hue and saturation can be rigorously defined. Moreover, the analysis of pure and mixed quantum chromatic states leads to a deep understanding of chromatic opposition and its role in the encoding of visual signals. We complete our paper by proving the existence of uncertainty relations for the degree of chromatic opposition, thus providing a theoretical confirmation of the quantum nature of color perception.

Multi-Grid Phase Field Skin Tumor Segmentation in 3D Ultrasound Images.

The aim of this paper is to present a new method for skin tumor segmentation in the 3D ultrasound images. We consider a variational formulation, the energy of which combines a diffuse interface phase field model (regularization term) and a log-likelihood computed using nonparametric estimates (data attachment term). We propose a multi-grid implementation with the exact solutions which has the advantage to avoid space discretization and numerical instabilities. The resulting algorithm is simple and easy to implement in multi-dimensions. Concerning applications, we focus on skin tumor segmentation. The clinical dataset used for the experiments is composed of 12 images with the ground truth given by a dermatologist. Comparisons with the reference methods show that the proposed method is more robust to the choice of the volume initialization. Moreover, thanks to the flexibility introduced by the diffuse interface, the sensitivity increases by 12% if the initialization is inside the lesion, and the Dice index increases by 59%, if the initialization covers the entire lesion. These results show that this new method is well designed to tackle the problem of underestimation of tumor volumes.