Color appearance model library

Create colors using CAM16 hue and chroma, L*a*b* L*,
and map them to RGB without distortion.

Test: atest FrameworksCoreTests:com.android.internal.graphics.cam
.CamTest, all passed. No link, atest/my build are broken and cannot
upload results.
Bug: 186640057
Change-Id: I64b605dd452d64e57be0047d2e4672917c01c2a8
This commit is contained in:
James O'Leary
2021-04-29 11:34:05 -04:00
parent a54b71543a
commit a23d054838
5 changed files with 1095 additions and 0 deletions

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@@ -22,6 +22,8 @@ import android.annotation.IntRange;
import android.annotation.NonNull;
import android.graphics.Color;
import com.android.internal.graphics.cam.Cam;
/**
* Copied from: frameworks/support/core-utils/java/android/support/v4/graphics/ColorUtils.java
*
@@ -332,6 +334,35 @@ public final class ColorUtils {
return Color.rgb(r, g, b);
}
/**
* Convert the ARGB color to a color appearance model.
*
* The color appearance model is based on CAM16 hue and chroma, using L*a*b*'s L* as the
* third dimension.
*
* @param color the ARGB color to convert. The alpha component is ignored.
*/
public static Cam colorToCAM(@ColorInt int color) {
return Cam.fromInt(color);
}
/**
* Convert a color appearance model representation to an ARGB color.
*
* Note: the returned color may have a lower chroma than requested. Whether a chroma is
* available depends on luminance. For example, there's no such thing as a high chroma light
* red, due to the limitations of our eyes and/or physics. If the requested chroma is
* unavailable, the highest possible chroma at the requested luminance is returned.
*
* @param hue hue, in degrees, in CAM coordinates
* @param chroma chroma in CAM coordinates.
* @param lstar perceptual luminance, L* in L*a*b*
*/
@ColorInt
public static int CAMToColor(float hue, float chroma, float lstar) {
return Cam.getInt(hue, chroma, lstar);
}
/**
* Set the alpha component of {@code color} to be {@code alpha}.
*/

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@@ -0,0 +1,509 @@
/*
* Copyright (C) 2021 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.android.internal.graphics.cam;
import android.annotation.NonNull;
import android.annotation.Nullable;
import com.android.internal.graphics.ColorUtils;
/**
* A color appearance model, based on CAM16, extended to use L* as the lightness dimension, and
* coupled to a gamut mapping algorithm. Creates a color system, enables a digital design system.
*/
public class Cam {
// The maximum difference between the requested L* and the L* returned.
private static final float DL_MAX = 0.2f;
// The maximum color distance, in CAM16-UCS, between a requested color and the color returned.
private static final float DE_MAX = 1.0f;
// When the delta between the floor & ceiling of a binary search for chroma is less than this,
// the binary search terminates.
private static final float CHROMA_SEARCH_ENDPOINT = 0.4f;
// When the delta between the floor & ceiling of a binary search for J, lightness in CAM16,
// is less than this, the binary search terminates.
private static final float LIGHTNESS_SEARCH_ENDPOINT = 0.01f;
// CAM16 color dimensions, see getters for documentation.
private final float mHue;
private final float mChroma;
private final float mJ;
private final float mQ;
private final float mM;
private final float mS;
// Coordinates in UCS space. Used to determine color distance, like delta E equations in L*a*b*.
private final float mJstar;
private final float mAstar;
private final float mBstar;
/** Hue in CAM16 */
public float getHue() {
return mHue;
}
/** Chroma in CAM16 */
public float getChroma() {
return mChroma;
}
/** Lightness in CAM16 */
public float getJ() {
return mJ;
}
/**
* Brightness in CAM16.
*
* <p>Prefer lightness, brightness is an absolute quantity. For example, a sheet of white paper
* is much brighter viewed in sunlight than in indoor light, but it is the lightest object under
* any lighting.
*/
public float getQ() {
return mQ;
}
/**
* Colorfulness in CAM16.
*
* <p>Prefer chroma, colorfulness is an absolute quantity. For example, a yellow toy car is much
* more colorful outside than inside, but it has the same chroma in both environments.
*/
public float getM() {
return mM;
}
/**
* Saturation in CAM16.
*
* <p>Colorfulness in proportion to brightness. Prefer chroma, saturation measures colorfulness
* relative to the color's own brightness, where chroma is colorfulness relative to white.
*/
public float getS() {
return mS;
}
/** Lightness coordinate in CAM16-UCS */
public float getJstar() {
return mJstar;
}
/** a* coordinate in CAM16-UCS */
public float getAstar() {
return mAstar;
}
/** b* coordinate in CAM16-UCS */
public float getBstar() {
return mBstar;
}
/** Construct a CAM16 color */
Cam(float hue, float chroma, float j, float q, float m, float s, float jstar, float astar,
float bstar) {
mHue = hue;
mChroma = chroma;
mJ = j;
mQ = q;
mM = m;
mS = s;
mJstar = jstar;
mAstar = astar;
mBstar = bstar;
}
/**
* Given a hue & chroma in CAM16, L* in L*a*b*, return an ARGB integer. The chroma of the color
* returned may, and frequently will, be lower than requested. Assumes the color is viewed in
* the
* frame defined by the sRGB standard.
*/
public static int getInt(float hue, float chroma, float lstar) {
return getInt(hue, chroma, lstar, Frame.DEFAULT);
}
/**
* Create a color appearance model from a ARGB integer representing a color. It is assumed the
* color was viewed in the frame defined in the sRGB standard.
*/
@NonNull
public static Cam fromInt(int argb) {
return fromIntInFrame(argb, Frame.DEFAULT);
}
/**
* Create a color appearance model from a ARGB integer representing a color, specifying the
* frame in which the color was viewed. Prefer Cam.fromInt.
*/
@NonNull
public static Cam fromIntInFrame(int argb, @NonNull Frame frame) {
// Transform ARGB int to XYZ
float[] xyz = CamUtils.xyzFromInt(argb);
// Transform XYZ to 'cone'/'rgb' responses
float[][] matrix = CamUtils.XYZ_TO_CAM16RGB;
float rT = (xyz[0] * matrix[0][0]) + (xyz[1] * matrix[0][1]) + (xyz[2] * matrix[0][2]);
float gT = (xyz[0] * matrix[1][0]) + (xyz[1] * matrix[1][1]) + (xyz[2] * matrix[1][2]);
float bT = (xyz[0] * matrix[2][0]) + (xyz[1] * matrix[2][1]) + (xyz[2] * matrix[2][2]);
// Discount illuminant
float rD = frame.getRgbD()[0] * rT;
float gD = frame.getRgbD()[1] * gT;
float bD = frame.getRgbD()[2] * bT;
// Chromatic adaptation
float rAF = (float) Math.pow(frame.getFl() * Math.abs(rD) / 100.0, 0.42);
float gAF = (float) Math.pow(frame.getFl() * Math.abs(gD) / 100.0, 0.42);
float bAF = (float) Math.pow(frame.getFl() * Math.abs(bD) / 100.0, 0.42);
float rA = Math.signum(rD) * 400.0f * rAF / (rAF + 27.13f);
float gA = Math.signum(gD) * 400.0f * gAF / (gAF + 27.13f);
float bA = Math.signum(bD) * 400.0f * bAF / (bAF + 27.13f);
// redness-greenness
float a = (float) (11.0 * rA + -12.0 * gA + bA) / 11.0f;
// yellowness-blueness
float b = (float) (rA + gA - 2.0 * bA) / 9.0f;
// auxiliary components
float u = (20.0f * rA + 20.0f * gA + 21.0f * bA) / 20.0f;
float p2 = (40.0f * rA + 20.0f * gA + bA) / 20.0f;
// hue
float atan2 = (float) Math.atan2(b, a);
float atanDegrees = atan2 * 180.0f / (float) Math.PI;
float hue =
atanDegrees < 0
? atanDegrees + 360.0f
: atanDegrees >= 360 ? atanDegrees - 360.0f : atanDegrees;
float hueRadians = hue * (float) Math.PI / 180.0f;
// achromatic response to color
float ac = p2 * frame.getNbb();
// CAM16 lightness and brightness
float j = 100.0f * (float) Math.pow(ac / frame.getAw(), frame.getC() * frame.getZ());
float q =
4.0f
/ frame.getC()
* (float) Math.sqrt(j / 100.0f)
* (frame.getAw() + 4.0f)
* frame.getFlRoot();
// CAM16 chroma, colorfulness, and saturation.
float huePrime = (hue < 20.14) ? hue + 360 : hue;
float eHue = 0.25f * (float) (Math.cos(huePrime * Math.PI / 180.0 + 2.0) + 3.8);
float p1 = 50000.0f / 13.0f * eHue * frame.getNc() * frame.getNcb();
float t = p1 * (float) Math.sqrt(a * a + b * b) / (u + 0.305f);
float alpha =
(float) Math.pow(t, 0.9) * (float) Math.pow(1.64 - Math.pow(0.29, frame.getN()),
0.73);
// CAM16 chroma, colorfulness, saturation
float c = alpha * (float) Math.sqrt(j / 100.0);
float m = c * frame.getFlRoot();
float s = 50.0f * (float) Math.sqrt((alpha * frame.getC()) / (frame.getAw() + 4.0f));
// CAM16-UCS components
float jstar = (1.0f + 100.0f * 0.007f) * j / (1.0f + 0.007f * j);
float mstar = 1.0f / 0.0228f * (float) Math.log(1.0f + 0.0228f * m);
float astar = mstar * (float) Math.cos(hueRadians);
float bstar = mstar * (float) Math.sin(hueRadians);
return new Cam(hue, c, j, q, m, s, jstar, astar, bstar);
}
/**
* Create a CAM from lightness, chroma, and hue coordinates. It is assumed those coordinates
* were measured in the sRGB standard frame.
*/
@NonNull
private static Cam fromJch(float j, float c, float h) {
return fromJchInFrame(j, c, h, Frame.DEFAULT);
}
/**
* Create a CAM from lightness, chroma, and hue coordinates, and also specify the frame in which
* the color is being viewed.
*/
@NonNull
private static Cam fromJchInFrame(float j, float c, float h, Frame frame) {
float q =
4.0f
/ frame.getC()
* (float) Math.sqrt(j / 100.0)
* (frame.getAw() + 4.0f)
* frame.getFlRoot();
float m = c * frame.getFlRoot();
float alpha = c / (float) Math.sqrt(j / 100.0);
float s = 50.0f * (float) Math.sqrt((alpha * frame.getC()) / (frame.getAw() + 4.0f));
float hueRadians = h * (float) Math.PI / 180.0f;
float jstar = (1.0f + 100.0f * 0.007f) * j / (1.0f + 0.007f * j);
float mstar = 1.0f / 0.0228f * (float) Math.log(1.0 + 0.0228 * m);
float astar = mstar * (float) Math.cos(hueRadians);
float bstar = mstar * (float) Math.sin(hueRadians);
return new Cam(h, c, j, q, m, s, jstar, astar, bstar);
}
/**
* Distance in CAM16-UCS space between two colors.
*
* <p>Much like L*a*b* was designed to measure distance between colors, the CAM16 standard
* defined a color space called CAM16-UCS to measure distance between CAM16 colors.
*/
public float distance(@NonNull Cam other) {
float dJ = getJstar() - other.getJstar();
float dA = getAstar() - other.getAstar();
float dB = getBstar() - other.getBstar();
double dEPrime = Math.sqrt(dJ * dJ + dA * dA + dB * dB);
double dE = 1.41 * Math.pow(dEPrime, 0.63);
return (float) dE;
}
/** Returns perceived color as an ARGB integer, as viewed in standard sRGB frame. */
public int viewedInSrgb() {
return viewed(Frame.DEFAULT);
}
/** Returns color perceived in a frame as an ARGB integer. */
public int viewed(@NonNull Frame frame) {
float alpha =
(getChroma() == 0.0 || getJ() == 0.0)
? 0.0f
: getChroma() / (float) Math.sqrt(getJ() / 100.0);
float t =
(float) Math.pow(alpha / Math.pow(1.64 - Math.pow(0.29, frame.getN()), 0.73),
1.0 / 0.9);
float hRad = getHue() * (float) Math.PI / 180.0f;
float eHue = 0.25f * (float) (Math.cos(hRad + 2.0) + 3.8);
float ac = frame.getAw() * (float) Math.pow(getJ() / 100.0,
1.0 / frame.getC() / frame.getZ());
float p1 = eHue * (50000.0f / 13.0f) * frame.getNc() * frame.getNcb();
float p2 = (ac / frame.getNbb());
float hSin = (float) Math.sin(hRad);
float hCos = (float) Math.cos(hRad);
float gamma =
23.0f * (p2 + 0.305f) * t / (23.0f * p1 + 11.0f * t * hCos + 108.0f * t * hSin);
float a = gamma * hCos;
float b = gamma * hSin;
float rA = (460.0f * p2 + 451.0f * a + 288.0f * b) / 1403.0f;
float gA = (460.0f * p2 - 891.0f * a - 261.0f * b) / 1403.0f;
float bA = (460.0f * p2 - 220.0f * a - 6300.0f * b) / 1403.0f;
float rCBase = (float) Math.max(0, (27.13 * Math.abs(rA)) / (400.0 - Math.abs(rA)));
float rC = Math.signum(rA) * (100.0f / frame.getFl()) * (float) Math.pow(rCBase,
1.0 / 0.42);
float gCBase = (float) Math.max(0, (27.13 * Math.abs(gA)) / (400.0 - Math.abs(gA)));
float gC = Math.signum(gA) * (100.0f / frame.getFl()) * (float) Math.pow(gCBase,
1.0 / 0.42);
float bCBase = (float) Math.max(0, (27.13 * Math.abs(bA)) / (400.0 - Math.abs(bA)));
float bC = Math.signum(bA) * (100.0f / frame.getFl()) * (float) Math.pow(bCBase,
1.0 / 0.42);
float rF = rC / frame.getRgbD()[0];
float gF = gC / frame.getRgbD()[1];
float bF = bC / frame.getRgbD()[2];
float[][] matrix = CamUtils.CAM16RGB_TO_XYZ;
float x = (rF * matrix[0][0]) + (gF * matrix[0][1]) + (bF * matrix[0][2]);
float y = (rF * matrix[1][0]) + (gF * matrix[1][1]) + (bF * matrix[1][2]);
float z = (rF * matrix[2][0]) + (gF * matrix[2][1]) + (bF * matrix[2][2]);
int argb = ColorUtils.XYZToColor(x, y, z);
return argb;
}
/**
* Given a hue & chroma in CAM16, L* in L*a*b*, and the frame in which the color will be
* viewed,
* return an ARGB integer.
*
* <p>The chroma of the color returned may, and frequently will, be lower than requested. This
* is
* a fundamental property of color that cannot be worked around by engineering. For example, a
* red
* hue, with high chroma, and high L* does not exist: red hues have a maximum chroma below 10
* in
* light shades, creating pink.
*/
public static int getInt(float hue, float chroma, float lstar, @NonNull Frame frame) {
// This is a crucial routine for building a color system, CAM16 itself is not sufficient.
//
// * Why these dimensions?
// Hue and chroma from CAM16 are used because they're the most accurate measures of those
// quantities. L* from L*a*b* is used because it correlates with luminance, luminance is
// used to measure contrast for a11y purposes, thus providing a key constraint on what
// colors
// can be used.
//
// * Why is this routine required to build a color system?
// In all perceptually accurate color spaces (i.e. L*a*b* and later), `chroma` may be
// impossible for a given `hue` and `lstar`.
// For example, a high chroma light red does not exist - chroma is limited to below 10 at
// light red shades, we call that pink. High chroma light green does exist, but not dark
// Also, when converting from another color space to RGB, the color may not be able to be
// represented in RGB. In those cases, the conversion process ends with RGB values
// outside 0-255
// The vast majority of color libraries surveyed simply round to 0 to 255. That is not an
// option for this library, as it distorts the expected luminance, and thus the expected
// contrast needed for a11y
//
// * What does this routine do?
// Dealing with colors in one color space not fitting inside RGB is, loosely referred to as
// gamut mapping or tone mapping. These algorithms are traditionally idiosyncratic, there is
// no universal answer. However, because the intent of this library is to build a system for
// digital design, and digital design uses luminance to measure contrast/a11y, we have one
// very important constraint that leads to an objective algorithm: the L* of the returned
// color _must_ match the requested L*.
//
// Intuitively, if the color must be distorted to fit into the RGB gamut, and the L*
// requested *must* be fulfilled, than the hue or chroma of the returned color will need
// to be different from the requested hue/chroma.
//
// After exploring both options, it was more intuitive that if the requested chroma could
// not be reached, it used the highest possible chroma. The alternative was finding the
// closest hue where the requested chroma could be reached, but that is not nearly as
// intuitive, as the requested hue is so fundamental to the color description.
// If the color doesn't have meaningful chroma, return a gray with the requested Lstar.
//
// Yellows are very chromatic at L = 100, and blues are very chromatic at L = 0. All the
// other hues are white at L = 100, and black at L = 0. To preserve consistency for users of
// this system, it is better to simply return white at L* > 99, and black and L* < 0.
if (chroma < 1.0 || Math.round(lstar) <= 0.0 || Math.round(lstar) >= 100.0) {
return CamUtils.intFromLstar(lstar);
}
hue = hue < 0 ? 0 : Math.min(360, hue);
// The highest chroma possible. Updated as binary search proceeds.
float high = chroma;
// The guess for the current binary search iteration. Starts off at the highest chroma,
// thus, if a color is possible at the requested chroma, the search can stop after one try.
float mid = chroma;
float low = 0.0f;
boolean isFirstLoop = true;
Cam answer = null;
while (Math.abs(low - high) >= CHROMA_SEARCH_ENDPOINT) {
// Given the current chroma guess, mid, and the desired hue, find J, lightness in
// CAM16 color space, that creates a color with L* = `lstar` in the L*a*b* color space.
Cam possibleAnswer = findCamByJ(hue, mid, lstar);
if (isFirstLoop) {
if (possibleAnswer != null) {
return possibleAnswer.viewed(frame);
} else {
// If this binary search iteration was the first iteration, and this point
// has been reached, it means the requested chroma was not available at the
// requested hue and L*.
// Proceed to a traditional binary search that starts at the midpoint between
// the requested chroma and 0.
isFirstLoop = false;
mid = low + (high - low) / 2.0f;
continue;
}
}
if (possibleAnswer == null) {
// There isn't a CAM16 J that creates a color with L* `lstar`. Try a lower chroma.
high = mid;
} else {
answer = possibleAnswer;
// It is possible to create a color. Try higher chroma.
low = mid;
}
mid = low + (high - low) / 2.0f;
}
// There was no answer: meaning, for the desired hue, there was no chroma low enough to
// generate a color with the desired L*.
// All values of L* are possible when there is 0 chroma. Return a color with 0 chroma, i.e.
// a shade of gray, with the desired L*.
if (answer == null) {
return CamUtils.intFromLstar(lstar);
}
return answer.viewed(frame);
}
// Find J, lightness in CAM16 color space, that creates a color with L* = `lstar` in the L*a*b*
// color space.
//
// Returns null if no J could be found that generated a color with L* `lstar`.
@Nullable
private static Cam findCamByJ(float hue, float chroma, float lstar) {
float low = 0.0f;
float high = 100.0f;
float mid = 0.0f;
float bestdL = 1000.0f;
float bestdE = 1000.0f;
Cam bestCam = null;
while (Math.abs(low - high) > LIGHTNESS_SEARCH_ENDPOINT) {
mid = low + (high - low) / 2;
// Create the intended CAM color
Cam camBeforeClip = Cam.fromJch(mid, chroma, hue);
// Convert the CAM color to RGB. If the color didn't fit in RGB, during the conversion,
// the initial RGB values will be outside 0 to 255. The final RGB values are clipped to
// 0 to 255, distorting the intended color.
int clipped = camBeforeClip.viewedInSrgb();
float clippedLstar = CamUtils.lstarFromInt(clipped);
float dL = Math.abs(lstar - clippedLstar);
// If the clipped color's L* is within error margin...
if (dL < DL_MAX) {
// ...check if the CAM equivalent of the clipped color is far away from intended CAM
// color. For the intended color, use lightness and chroma from the clipped color,
// and the intended hue. Callers are wondering what the lightness is, they know
// chroma may be distorted, so the only concern here is if the hue slipped too far.
Cam camClipped = Cam.fromInt(clipped);
float dE = camClipped.distance(
Cam.fromJch(camClipped.getJ(), camClipped.getChroma(), hue));
if (dE <= DE_MAX) {
bestdL = dL;
bestdE = dE;
bestCam = camClipped;
}
}
// If there's no error at all, there's no need to search more.
//
// Note: this happens much more frequently than expected, but this is a very delicate
// property which relies on extremely precise sRGB <=> XYZ calculations, as well as fine
// tuning of the constants that determine error margins and when the binary search can
// terminate.
if (bestdL == 0 && bestdE == 0) {
break;
}
if (clippedLstar < lstar) {
low = mid;
} else {
high = mid;
}
}
return bestCam;
}
}

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/*
* Copyright (C) 2021 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.android.internal.graphics.cam;
import android.annotation.NonNull;
import android.graphics.Color;
import com.android.internal.graphics.ColorUtils;
/**
* Collection of methods for transforming between color spaces.
*
* <p>Methods are named $xFrom$Y. For example, lstarFromInt() returns L* from an ARGB integer.
*
* <p>These methods, generally, convert colors between the L*a*b*, XYZ, and sRGB spaces.
*
* <p>L*a*b* is a perceptually accurate color space. This is particularly important in the L*
* dimension: it measures luminance and unlike lightness measures traditionally used in UI work via
* RGB or HSL, this luminance transitions smoothly, permitting creation of pleasing shades of a
* color, and more pleasing transitions between colors.
*
* <p>XYZ is commonly used as an intermediate color space for converting between one color space to
* another. For example, to convert RGB to L*a*b*, first RGB is converted to XYZ, then XYZ is
* convered to L*a*b*.
*
* <p>sRGB is a "specification originated from work in 1990s through cooperation by Hewlett-Packard
* and Microsoft, and it was designed to be a standard definition of RGB for the internet, which it
* indeed became...The standard is based on a sampling of computer monitors at the time...The whole
* idea of sRGB is that if everyone assumed that RGB meant the same thing, then the results would be
* consistent, and reasonably good. It worked." - Fairchild, Color Models and Systems: Handbook of
* Color Psychology, 2015
*/
public final class CamUtils {
private CamUtils() {
}
// Transforms XYZ color space coordinates to 'cone'/'RGB' responses in CAM16.
static final float[][] XYZ_TO_CAM16RGB = {
{0.401288f, 0.650173f, -0.051461f},
{-0.250268f, 1.204414f, 0.045854f},
{-0.002079f, 0.048952f, 0.953127f}
};
// Transforms 'cone'/'RGB' responses in CAM16 to XYZ color space coordinates.
static final float[][] CAM16RGB_TO_XYZ = {
{1.86206786f, -1.01125463f, 0.14918677f},
{0.38752654f, 0.62144744f, -0.00897398f},
{-0.01584150f, -0.03412294f, 1.04996444f}
};
// Need this, XYZ coordinates in internal ColorUtils are private
// sRGB specification has D65 whitepoint - Stokes, Anderson, Chandrasekar, Motta - A Standard
// Default Color Space for the Internet: sRGB, 1996
static final float[] WHITE_POINT_D65 = {95.047f, 100.0f, 108.883f};
// This is a more precise sRGB to XYZ transformation matrix than traditionally
// used. It was derived using Schlomer's technique of transforming the xyY
// primaries to XYZ, then applying a correction to ensure mapping from sRGB
// 1, 1, 1 to the reference white point, D65.
static final float[][] SRGB_TO_XYZ = {
{0.41233895f, 0.35762064f, 0.18051042f},
{0.2126f, 0.7152f, 0.0722f},
{0.01932141f, 0.11916382f, 0.95034478f}
};
static int intFromLstar(float lstar) {
if (lstar < 1) {
return 0xff000000;
} else if (lstar > 99) {
return 0xffffffff;
}
// XYZ to LAB conversion routine, assume a and b are 0.
float fy = (lstar + 16.0f) / 116.0f;
// fz = fx = fy because a and b are 0
float fz = fy;
float fx = fy;
float kappa = 24389f / 27f;
float epsilon = 216f / 24389f;
boolean lExceedsEpsilonKappa = (lstar > 8.0f);
float yT = lExceedsEpsilonKappa ? fy * fy * fy : lstar / kappa;
boolean cubeExceedEpsilon = (fy * fy * fy) > epsilon;
float xT = cubeExceedEpsilon ? fx * fx * fx : (116f * fx - 16f) / kappa;
float zT = cubeExceedEpsilon ? fz * fz * fz : (116f * fx - 16f) / kappa;
return ColorUtils.XYZToColor(xT * CamUtils.WHITE_POINT_D65[0],
yT * CamUtils.WHITE_POINT_D65[1], zT * CamUtils.WHITE_POINT_D65[2]);
}
/** Returns L* from L*a*b*, perceptual luminance, from an ARGB integer (ColorInt). */
public static float lstarFromInt(int argb) {
return lstarFromY(yFromInt(argb));
}
static float lstarFromY(float y) {
y = y / 100.0f;
final float e = 216.f / 24389.f;
float yIntermediate;
if (y <= e) {
return ((24389.f / 27.f) * y);
} else {
yIntermediate = (float) Math.cbrt(y);
}
return 116.f * yIntermediate - 16.f;
}
static float yFromInt(int argb) {
final float r = linearized(Color.red(argb));
final float g = linearized(Color.green(argb));
final float b = linearized(Color.blue(argb));
float[][] matrix = SRGB_TO_XYZ;
float y = (r * matrix[1][0]) + (g * matrix[1][1]) + (b * matrix[1][2]);
return y;
}
@NonNull
static float[] xyzFromInt(int argb) {
final float r = linearized(Color.red(argb));
final float g = linearized(Color.green(argb));
final float b = linearized(Color.blue(argb));
float[][] matrix = SRGB_TO_XYZ;
float x = (r * matrix[0][0]) + (g * matrix[0][1]) + (b * matrix[0][2]);
float y = (r * matrix[1][0]) + (g * matrix[1][1]) + (b * matrix[1][2]);
float z = (r * matrix[2][0]) + (g * matrix[2][1]) + (b * matrix[2][2]);
return new float[]{x, y, z};
}
static float yFromLstar(float lstar) {
float ke = 8.0f;
if (lstar > ke) {
return (float) Math.pow(((lstar + 16.0) / 116.0), 3) * 100f;
} else {
return lstar / (24389f / 27f) * 100f;
}
}
static float linearized(int rgbComponent) {
float normalized = (float) rgbComponent / 255.0f;
if (normalized <= 0.04045f) {
return (normalized / 12.92f) * 100.0f;
} else {
return (float) Math.pow(((normalized + 0.055f) / 1.055f), 2.4f) * 100.0f;
}
}
}

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/*
* Copyright (C) 2021 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.android.internal.graphics.cam;
import android.annotation.NonNull;
import android.util.MathUtils;
/**
* The frame, or viewing conditions, where a color was seen. Used, along with a color, to create a
* color appearance model representing the color.
*
* <p>To convert a traditional color to a color appearance model, it requires knowing what
* conditions the color was observed in. Our perception of color depends on, for example, the tone
* of the light illuminating the color, how bright that light was, etc.
*
* <p>This class is modelled separately from the color appearance model itself because there are a
* number of calculations during the color => CAM conversion process that depend only on the viewing
* conditions. Caching those calculations in a Frame instance saves a significant amount of time.
*/
public final class Frame {
// Standard viewing conditions assumed in RGB specification - Stokes, Anderson, Chandrasekar,
// Motta - A Standard Default Color Space for the Internet: sRGB, 1996.
//
// White point = D65
// Luminance of adapting field: 200 / Pi / 5, units are cd/m^2.
// sRGB ambient illuminance = 64 lux (per sRGB spec). However, the spec notes this is
// artificially low and based on monitors in 1990s. Use 200, the sRGB spec says this is the
// real average, and a survey of lux values on Wikipedia confirms this is a comfortable
// default: somewhere between a very dark overcast day and office lighting.
// Per CAM16 introduction paper (Li et al, 2017) Ew = pi * lw, and La = lw * Yb/Yw
// Ew = ambient environment luminance, in lux.
// Yb/Yw is taken to be midgray, ~20% relative luminance (XYZ Y 18.4, CIELAB L* 50).
// Therefore La = (Ew / pi) * .184
// La = 200 / pi * .184
// Image surround to 10 degrees = ~20% relative luminance = CIELAB L* 50
//
// Not from sRGB standard:
// Surround = average, 2.0.
// Discounting illuminant = false, doesn't occur for self-luminous displays
public static final Frame DEFAULT =
Frame.make(
CamUtils.WHITE_POINT_D65,
(float) (200.0f / Math.PI * CamUtils.yFromLstar(50.0f) / 100.f), 50.0f, 2.0f,
false);
private final float mAw;
private final float mNbb;
private final float mNcb;
private final float mC;
private final float mNc;
private final float mN;
private final float[] mRgbD;
private final float mFl;
private final float mFlRoot;
private final float mZ;
float getAw() {
return mAw;
}
float getN() {
return mN;
}
float getNbb() {
return mNbb;
}
float getNcb() {
return mNcb;
}
float getC() {
return mC;
}
float getNc() {
return mNc;
}
@NonNull
float[] getRgbD() {
return mRgbD;
}
float getFl() {
return mFl;
}
float getFlRoot() {
return mFlRoot;
}
float getZ() {
return mZ;
}
private Frame(float n, float aw, float nbb, float ncb, float c, float nc, float[] rgbD,
float fl, float fLRoot, float z) {
mN = n;
mAw = aw;
mNbb = nbb;
mNcb = ncb;
mC = c;
mNc = nc;
mRgbD = rgbD;
mFl = fl;
mFlRoot = fLRoot;
mZ = z;
}
/** Create a custom frame. */
@NonNull
public static Frame make(@NonNull float[] whitepoint, float adaptingLuminance,
float backgroundLstar, float surround, boolean discountingIlluminant) {
// Transform white point XYZ to 'cone'/'rgb' responses
float[][] matrix = CamUtils.XYZ_TO_CAM16RGB;
float[] xyz = whitepoint;
float rW = (xyz[0] * matrix[0][0]) + (xyz[1] * matrix[0][1]) + (xyz[2] * matrix[0][2]);
float gW = (xyz[0] * matrix[1][0]) + (xyz[1] * matrix[1][1]) + (xyz[2] * matrix[1][2]);
float bW = (xyz[0] * matrix[2][0]) + (xyz[1] * matrix[2][1]) + (xyz[2] * matrix[2][2]);
// Scale input surround, domain (0, 2), to CAM16 surround, domain (0.8, 1.0)
float f = 0.8f + (surround / 10.0f);
// "Exponential non-linearity"
float c = (f >= 0.9) ? MathUtils.lerp(0.59f, 0.69f, ((f - 0.9f) * 10.0f)) : MathUtils.lerp(
0.525f, 0.59f, ((f - 0.8f) * 10.0f));
// Calculate degree of adaptation to illuminant
float d = discountingIlluminant ? 1.0f : f * (1.0f - ((1.0f / 3.6f) * (float) Math.exp(
(-adaptingLuminance - 42.0f) / 92.0f)));
// Per Li et al, if D is greater than 1 or less than 0, set it to 1 or 0.
d = (d > 1.0) ? 1.0f : (d < 0.0) ? 0.0f : d;
// Chromatic induction factor
float nc = f;
// Cone responses to the whitepoint, adjusted for illuminant discounting.
//
// Why use 100.0 instead of the white point's relative luminance?
//
// Some papers and implementations, for both CAM02 and CAM16, use the Y
// value of the reference white instead of 100. Fairchild's Color Appearance
// Models (3rd edition) notes that this is in error: it was included in the
// CIE 2004a report on CIECAM02, but, later parts of the conversion process
// account for scaling of appearance relative to the white point relative
// luminance. This part should simply use 100 as luminance.
float[] rgbD = new float[]{d * (100.0f / rW) + 1.0f - d, d * (100.0f / gW) + 1.0f - d,
d * (100.0f / bW) + 1.0f - d, };
// Luminance-level adaptation factor
float k = 1.0f / (5.0f * adaptingLuminance + 1.0f);
float k4 = k * k * k * k;
float k4F = 1.0f - k4;
float fl = (k4 * adaptingLuminance) + (0.1f * k4F * k4F * (float) Math.cbrt(
5.0 * adaptingLuminance));
// Intermediate factor, ratio of background relative luminance to white relative luminance
float n = CamUtils.yFromLstar(backgroundLstar) / whitepoint[1];
// Base exponential nonlinearity
// note Schlomer 2018 has a typo and uses 1.58, the correct factor is 1.48
float z = 1.48f + (float) Math.sqrt(n);
// Luminance-level induction factors
float nbb = 0.725f / (float) Math.pow(n, 0.2);
float ncb = nbb;
// Discounted cone responses to the white point, adjusted for post-chromatic
// adaptation perceptual nonlinearities.
float[] rgbAFactors = new float[]{(float) Math.pow(fl * rgbD[0] * rW / 100.0, 0.42),
(float) Math.pow(fl * rgbD[1] * gW / 100.0, 0.42), (float) Math.pow(
fl * rgbD[2] * bW / 100.0, 0.42)};
float[] rgbA = new float[]{(400.0f * rgbAFactors[0]) / (rgbAFactors[0] + 27.13f),
(400.0f * rgbAFactors[1]) / (rgbAFactors[1] + 27.13f),
(400.0f * rgbAFactors[2]) / (rgbAFactors[2] + 27.13f), };
float aw = ((2.0f * rgbA[0]) + rgbA[1] + (0.05f * rgbA[2])) * nbb;
return new Frame(n, aw, nbb, ncb, c, nc, rgbD, fl, (float) Math.pow(fl, 0.25), z);
}
}

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/*
* Copyright (C) 2021 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.android.internal.graphics.cam;
import static org.junit.Assert.assertEquals;
import org.junit.Test;
import org.junit.runner.RunWith;
import org.junit.runners.JUnit4;
@RunWith(JUnit4.class)
public final class CamTest {
static final int BLACK = 0xff000000;
static final int WHITE = 0xffffffff;
static final int MIDGRAY = 0xff777777;
static final int RED = 0xffff0000;
static final int GREEN = 0xff00ff00;
static final int BLUE = 0xff0000ff;
@Test
public void camFromIntToInt() {
Cam cam = Cam.fromInt(RED);
int color = cam.viewed(Frame.DEFAULT);
assertEquals(color, RED);
}
@Test
public void yFromMidgray() {
assertEquals(18.418f, CamUtils.yFromLstar(50.0f), 0.001);
}
@Test
public void yFromBlack() {
assertEquals(0.0f, CamUtils.yFromLstar(0.0f), 0.001);
}
@Test
public void yFromWhite() {
assertEquals(100.0f, CamUtils.yFromLstar(100.0f), 0.001);
}
@Test
public void camFromRed() {
Cam cam = Cam.fromInt(RED);
assertEquals(46.445f, cam.getJ(), 0.001f);
assertEquals(113.357f, cam.getChroma(), 0.001f);
assertEquals(27.408f, cam.getHue(), 0.001f);
assertEquals(89.494f, cam.getM(), 0.001f);
assertEquals(91.889f, cam.getS(), 0.001f);
assertEquals(105.988f, cam.getQ(), 0.001f);
}
@Test
public void camFromGreen() {
Cam cam = Cam.fromInt(GREEN);
assertEquals(79.331f, cam.getJ(), 0.001f);
assertEquals(108.409f, cam.getChroma(), 0.001f);
assertEquals(142.139f, cam.getHue(), 0.001f);
assertEquals(85.587f, cam.getM(), 0.001f);
assertEquals(78.604f, cam.getS(), 0.001f);
assertEquals(138.520, cam.getQ(), 0.001f);
}
@Test
public void camFromBlue() {
Cam cam = Cam.fromInt(BLUE);
assertEquals(25.465f, cam.getJ(), 0.001f);
assertEquals(87.230f, cam.getChroma(), 0.001f);
assertEquals(282.788f, cam.getHue(), 0.001f);
assertEquals(68.867f, cam.getM(), 0.001f);
assertEquals(93.674f, cam.getS(), 0.001f);
assertEquals(78.481f, cam.getQ(), 0.001f);
}
@Test
public void camFromBlack() {
Cam cam = Cam.fromInt(BLACK);
assertEquals(0.0f, cam.getJ(), 0.001f);
assertEquals(0.0f, cam.getChroma(), 0.001f);
assertEquals(0.0f, cam.getHue(), 0.001f);
assertEquals(0.0f, cam.getM(), 0.001f);
assertEquals(0.0f, cam.getS(), 0.001f);
assertEquals(0.0f, cam.getQ(), 0.001f);
}
@Test
public void camFromWhite() {
Cam cam = Cam.fromInt(WHITE);
assertEquals(100.0f, cam.getJ(), 0.001f);
assertEquals(2.869f, cam.getChroma(), 0.001f);
assertEquals(209.492f, cam.getHue(), 0.001f);
assertEquals(2.265f, cam.getM(), 0.001f);
assertEquals(12.068f, cam.getS(), 0.001f);
assertEquals(155.521, cam.getQ(), 0.001f);
}
@Test
public void getRedFromGamutMap() {
int colorToTest = RED;
Cam cam = Cam.fromInt(colorToTest);
int color = Cam.getInt(cam.getHue(), cam.getChroma(), CamUtils.lstarFromInt(colorToTest));
assertEquals(colorToTest, color);
}
@Test
public void getGreenFromGamutMap() {
int colorToTest = GREEN;
Cam cam = Cam.fromInt(colorToTest);
int color = Cam.getInt(cam.getHue(), cam.getChroma(), CamUtils.lstarFromInt(colorToTest));
assertEquals(colorToTest, color);
}
@Test
public void getBlueFromGamutMap() {
int colorToTest = BLUE;
Cam cam = Cam.fromInt(colorToTest);
int color = Cam.getInt(cam.getHue(), cam.getChroma(), CamUtils.lstarFromInt(colorToTest));
assertEquals(colorToTest, color);
}
@Test
public void getWhiteFromGamutMap() {
int colorToTest = WHITE;
Cam cam = Cam.fromInt(colorToTest);
int color = Cam.getInt(cam.getHue(), cam.getChroma(), CamUtils.lstarFromInt(colorToTest));
assertEquals(colorToTest, color);
}
@Test
public void getBlackFromGamutMap() {
int colorToTest = BLACK;
Cam cam = Cam.fromInt(colorToTest);
int color = Cam.getInt(cam.getHue(), cam.getChroma(), CamUtils.lstarFromInt(colorToTest));
assertEquals(colorToTest, color);
}
@Test
public void getMidgrayFromGamutMap() {
int colorToTest = MIDGRAY;
Cam cam = Cam.fromInt(colorToTest);
int color = Cam.getInt(cam.getHue(), cam.getChroma(), CamUtils.lstarFromInt(colorToTest));
assertEquals(colorToTest, color);
}
@Test
public void getRandomGreenFromGamutMap() {
int colorToTest = 0xff009200;
Cam cam = Cam.fromInt(colorToTest);
int color = Cam.getInt(cam.getHue(), cam.getChroma(), CamUtils.lstarFromInt(colorToTest));
assertEquals(colorToTest, color);
}
@Test
public void gamutMapArbitraryHCL() {
int color = Cam.getInt(309.0f, 40.0f, 70.0f);
Cam cam = Cam.fromInt(color);
assertEquals(308.759f, cam.getHue(), 0.001);
assertEquals(40.148f, cam.getChroma(), 0.001);
assertEquals(70.029f, CamUtils.lstarFromInt(color), 0.001f);
}
@Test
public void ucsCoordinates() {
Cam cam = Cam.fromInt(RED);
assertEquals(59.584f, cam.getJstar(), 0.001f);
assertEquals(43.297f, cam.getAstar(), 0.001f);
assertEquals(22.451f, cam.getBstar(), 0.001f);
}
@Test
public void deltaEWhiteToBlack() {
assertEquals(25.661f, Cam.fromInt(WHITE).distance(Cam.fromInt(BLACK)), 0.001f);
}
@Test
public void deltaERedToBlue() {
assertEquals(21.415f, Cam.fromInt(RED).distance(Cam.fromInt(BLUE)), 0.001f);
}
}