PubMed Health⌕ Search
Home/Archive/PubMed

PubMed · 16396021

Mathematical definition and analysis of the retinex algorithm.

Edoardo Provenzi·Luca De Carli·Alessandro Rizzi·Daniele Marini
View original source ↗Export metadata ↓

Abstract

We present a detailed mathematical analysis of the original Retinex algorithm due to Land and McCann [J. Opt. Soc. Am. 61, 1 (1071)]. To this end, we propose an analytic formula that describes the algorithm behavior. More than one Retinex version (e.g., with and without threshold) is examined. The behavior of Retinex varying the number of paths is predicted, and its recursive iterations are mathematically analyzed using the formula. The mathematical setting presented serves as a common ground for the various Retinex implementations. Its validity is confirmed by the tests on images that we have performed.

Explore related subjects

Color PerceptionComputer SimulationHumansModels, BiologicalRetinaSensory ThresholdsJournal Article

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Edoardo Provenzi, Luca De Carli, Alessandro Rizzi, Daniele Marini. 2005. Mathematical definition and analysis of the retinex algorithm.. https://doi.org/10.1364/josaa.22.002613

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2006

Discrete color filling beyond luminance gaps along perceptual surfaces.

Perceived color at a point in space is not determined simply by the color directly stimulating the corresponding retinal position. Surface color is informed by flanking edge signals, which also serve to inhibit the intrusion of signals from neighboring surfaces. Spatially continuous local interactions among color and luminance signals have been implicated in a propagation process often referred to as filling-in. Here, we report a phenomenon of discrete color filling whereby color jumps over luminance gaps filling into disconnected regions of the stimulus. This color filling is found to be blocked at boundaries defined by texture. The color filling is also highly specific to the elements belonging to a common perceptual surface, even when multiple surfaces are transparently overlaid. Our results indicate that color filling can be governed by a host of visual cues outside the realm of first-order color and brightness, via their impact on perceptual surface segmentation and segregation.

Color Perception↗
PubMed2006

Combining local and global contributions to perceived colour: an analysis of the variability in symmetric and asymmetric colour matching.

Are surfaces' colours judged from weighted averages of the light that they reflect to the eyes and the colour contrast at their borders? To find out we asked subjects to set the colour and luminance of test disks to match reference disks, on various backgrounds, and analysed the variability in their settings. Most of the variability between repeated settings was in luminance. The standard deviations in the set colour were smallest when the disk and background were the same colour, irrespective of the colour itself. Matches were equally precise for greenish or reddish disks on a grey background, as for grey disks on a greenish or reddish background. The precision was less dependent on the colour contrast at the disks' borders when the backgrounds were more complex and when there was a large luminance contrast at the disks' borders. Subjects were less precise when different colours surrounded the two disks. These findings are consistent with the perceived colour at any position being a weighted average of the local cone excitation ratio and the change in the cone excitation ratio at the borders of the surface in question. However, the involved weights must be variable and depend systematically on parameters such as the luminance contrast at the surface's borders and other chromatic contrasts within the scene.

Color Perception↗
PubMed2006

Modularity beyond perception: evidence from single task interference paradigms.

We combine the Dimension-Action (DA) model with translational models to account for both the Stroop and the flanker effects. The basic assumption of the model is that there are distinct visual modules, each of which is endowed with both perception and response selection processes. We contrast this model with an alternative widespread view, the standard view, according to which the same response selection processes are shared by all tasks. The two views have different predictions concerning the flanker and Stroop tasks. Seven experiments test these predictions. The first five experiments show that there is a fundamental difference between the typical Stroop and flanker effects. Moreover, these experiments show that words denoting colors can affect print colors only when they are required for naming or when participants verbally mediate the print color task. Experiments 6 and 7 show that an analogous interaction between color and shape exists in the flanker task. These experiments as well as previous studies are consistent with the DA model and the modular view and pose serious difficulties for the standard view. Wider implications of a visual modular architecture are discussed as well.

Color Perception↗