Paper: Schaefer, Hordley, =
and Finlayson,=C2=A0"A combined physical and statistical approa=
ch to colour constancy", *CVPR*, 2005.

Summary by Marius = Orehovschi and Dhruv Joshi

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In this paper, the authors de= scribe approaches for computational color constancy, the problem of estimat= ing the scene illuminant given one image. They describe two main categories= of approaches to this problem: statistics-based methods that use the insig= ht that colors observed in the image constrain the set of possible illumina= nts, and physics-based methods that use the dichromatic reflectance model. = Both of these categories of methods yield not just a single most likely ill= uminant, but a set of possible illuminants along with their respective prob= abilities. The main finding of the paper is that combining these approaches= results in better performance than either one of the two categories of met= hods, with a reduction in error of at least 20%.

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The statistical method:

The color of each pixel gives a better understandi= ng to the algorithm on what color illuminant is for the scene in the image.= A statistical method uses color by correlation which uses the color of the= pixels to estimate the probability of each of N illuminants. Thus, using a= Bayesian probability method, the model builds a vector that suggests the p= robabilities for each of the N illuminants.

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This is done in 5 m= ain steps: choosing the color space, characterizing most realistic illumina= nts that could reasonably be encountered in the image (both of which only n= eed to be done once for a device), characterizing the input image, correlat= ing the image information with the illuminant characteristics to predict a = log probability for each of the N illuminants, and then finally selecting t= he best illuminant based on these probabilities.=C2=A0

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The phys= ics-based method:

The physi= cs based method for determining the illuminant is based on the insight that= the color signals of a dichromatic object fall on a two-dimensional plane = in the RGB space which contains the illumination vector. Two such objects w= ould yield two planes and their intersection would represent the illuminati= on vector. When estimating the illuminant based on more than two surfaces, = the illuminant is considered the =E2=80=9Cbest=E2=80=9D intersection of the= planes, where =E2=80=9Cbest=E2=80=9D is the least-squares solution to an e= igenvector problem.=C2=A0

But this intuitive model has been sho= wn to rarely translate well into practice =E2=80=93 noise and insufficient = segmentation make it so that the model only works well under strict laborat= ory conditions, with highly saturated surfaces and controlled lighting. The= authors propose a more robust method that involves comparing the intersect= ions of pairs of planes. This allows for the elimination of unstable or unl= ikely results. For example, the intersection of two planes with similar ori= entation has been proven to be unstable; thus, an intersection of two plane= s that are separated by an angle smaller than a certain preselected value a= re ruled out. On the other hand, an intersection that is too far away from = the convex hull of likely illuminants is unlikely to describe a plausible i= lluminant; thus, intersections that form an angle above a certain preselect= ed value with any vector in the convex hull of likely illuminants are also = ruled out.=C2=A0

The likely illuminants are then selected from = the remaining intersections by a method similar to finding the nearest neig= hbors to a set of preselected reference lights. But because two intersectio= ns can be equally far away from a reference light, neither one would get th= e vote in this scenario. Thus, the authors propose an alternative method = =E2=80=93 increment the likelihood of each illuminant by the inverse of the= distance between the intersection and the reference light.=C2=A0

Similarly to the correlation method, the physical approach to color cons= tancy provides more than just the most likely illuminant =E2=80=93 it provi= des a set of likely illuminants and their respective likelihoods.

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Combining the two:

The authors use a straight-forward approach to combining t=
he results of the two methods: the final result contains the vectors produc=
ed by the two methods along with their respective probabilities, where the =
probability of an illumination vector is simply a weighted sum of the proba=
bilities yielded by the two methods for the particular vector.

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Strengths of the paper and the proposed techni= ques:

- The authors outline a combination of two strong algorithms that=
individually performed well and are fast, understandable, and have good re=
sults. Linearly combining these two algorithms, the results of the authors =
are still fast, understandable, and get better results than the individual =
algorithms.
- The explanation of the methods is accessible and well-organized: the au=
thors first present a simpler, more intuitive model; then they acknowledge =
its limitations and present a more robust and sophisticated model that the =
reader can digest more easily after having understood the simpler model fir=
st.
- = =C2=A0The paper also addresses the fact = that even though the improvements in the table look small, they are equival= ent to a near 20% improvement to the predecessors.
- The authors could have provided more data tables and more results = to illustrate the improvements in performance of the new approach; they cou= ld have also organized table 1 by dataset, so that it is easier to make app= les-to-apples comparisons.
- Altho= ugh the paper uses the two algorithms to get better results, the paper does= not introduce any significant novel concepts other than the combination of= the two previously existing approaches.
- Although the authors show an improvement in performance ove= r previously developed methods on two very particular datasets, they do not= address how this improvement translates to real-world situations.

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Weaknesses and limitations:

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Overall, t= he paper proposes an important finding and is well-written and accessible. = The paper also clearly shows connections to previous work =E2=80=93 its new= approach is based on combining previously developed methods. The descripti= on of the methods is thorough and makes it possible for a qualified reader = to reproduce the results in practice. The authors address the fact that the= improvements might look small at first sight and show why they are actuall= y significant, with the reduction in error being over 20%. Although the pap= er's main finding is a simple one, the significant improvement in results d= eems its simplicity more a strength than a weakness.

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