sorting - How to sort colors properly?

I can't seem to be able to sort colors by their hue and perceptual brightness correctly. Here's my current solution, but it's not right; there are all these dark bands:

c = RandomColor[RGBColor[_, _, _], 500];
o1 = SortBy[c, ColorConvert[#, "HSB"][[1]] &];
o2 = SortBy[c, ColorConvert[#, "LAB"][[2]] &];
Image[#, ImageSize -> 400] & /@ {Table[o1, {100}], Table[o2, {100}]}

my attempt to sort colors

I want to find a way to achieve color sorting that minimizes these bands and smooths the transition along the gradient, something similar to the clustering histograms Theo Gray used in the Disney app.

clustering histograms

Answer

If you're looking for a way to sort the colors in such a way as to make them seem the least discontinuous, then one way to think of it is that each color is a point in a space endowed with a distance metric (either the CIELAB 1976 or the CIELAB2000 perceptual metrics), and you are trying to find a shortest tour that visits each point. We can do that with ColorDistance and FindShortestTour:

c = RandomColor[500];
ord2000 = 
  FindShortestTour[c, 
    DistanceFunction -> (ColorDistance[#1, #2, 
        DistanceFunction -> "CIE2000"] &)][[2]];

ord76 = FindShortestTour[c, DistanceFunction -> ColorDistance][[2]];
Image[Table[c[[ord2000]], {100}]]
Image[Table[c[[ord76]], {100}]]

Giving the following two results:

enter image description here

To my eye, it looks like the CIE2000 metric does a slightly better job than the older 1976 variant.

As Mr. Wizard points out, "sorting" colors is sort of like "sorting" random points in a space with more than one dimension: there's no general way to do it that makes sense, since you're trying to impose a linear order on something which has more than one dimension. So the best you can do is find a shortest tour.

Comments

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.

Blog

Search This Blog