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// This file is available under and governed by the GNU General Public
// License version 2 only, as published by the Free Software Foundation.
// However, the following notice accompanied the original version of this
// file:
//
//---------------------------------------------------------------------------------
//
// Little Color Management System
// Copyright (c) 1998-2012 Marti Maria Saguer
//
// Permission is hereby granted, free of charge, to any person obtaining
// a copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the Software
// is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO
// THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
// LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
//
//---------------------------------------------------------------------------------
//
#include "lcms2_internal.h"
// Tone curves are powerful constructs that can contain curves specified in diverse ways.
// The curve is stored in segments, where each segment can be sampled or specified by parameters.
// a 16.bit simplification of the *whole* curve is kept for optimization purposes. For float operation,
// each segment is evaluated separately. Plug-ins may be used to define new parametric schemes,
// each plug-in may define up to MAX_TYPES_IN_LCMS_PLUGIN functions types. For defining a function,
// the plug-in should provide the type id, how many parameters each type has, and a pointer to
// a procedure that evaluates the function. In the case of reverse evaluation, the evaluator will
// be called with the type id as a negative value, and a sampled version of the reversed curve
// will be built.
// ----------------------------------------------------------------- Implementation
// Maxim number of nodes
#define MAX_NODES_IN_CURVE 4097
#define MINUS_INF (-1E22F)
#define PLUS_INF (+1E22F)
// The list of supported parametric curves
typedef struct _cmsParametricCurvesCollection_st {
int nFunctions; // Number of supported functions in this chunk
int FunctionTypes[MAX_TYPES_IN_LCMS_PLUGIN]; // The identification types
int ParameterCount[MAX_TYPES_IN_LCMS_PLUGIN]; // Number of parameters for each function
cmsParametricCurveEvaluator Evaluator; // The evaluator
struct _cmsParametricCurvesCollection_st* Next; // Next in list
} _cmsParametricCurvesCollection;
// This is the default (built-in) evaluator
static cmsFloat64Number DefaultEvalParametricFn(cmsInt32Number Type, const cmsFloat64Number Params[], cmsFloat64Number R);
// The built-in list
static _cmsParametricCurvesCollection DefaultCurves = {
9, // # of curve types
{ 1, 2, 3, 4, 5, 6, 7, 8, 108 }, // Parametric curve ID
{ 1, 3, 4, 5, 7, 4, 5, 5, 1 }, // Parameters by type
DefaultEvalParametricFn, // Evaluator
NULL // Next in chain
};
// The linked list head
static _cmsParametricCurvesCollection* ParametricCurves = &DefaultCurves;
// As a way to install new parametric curves
cmsBool _cmsRegisterParametricCurvesPlugin(cmsPluginBase* Data)
{
cmsPluginParametricCurves* Plugin = (cmsPluginParametricCurves*) Data;
_cmsParametricCurvesCollection* fl;
if (Data == NULL) {
ParametricCurves = &DefaultCurves;
return TRUE;
}
fl = (_cmsParametricCurvesCollection*) _cmsPluginMalloc(sizeof(_cmsParametricCurvesCollection));
if (fl == NULL) return FALSE;
// Copy the parameters
fl ->Evaluator = Plugin ->Evaluator;
fl ->nFunctions = Plugin ->nFunctions;
// Make sure no mem overwrites
if (fl ->nFunctions > MAX_TYPES_IN_LCMS_PLUGIN)
fl ->nFunctions = MAX_TYPES_IN_LCMS_PLUGIN;
// Copy the data
memmove(fl->FunctionTypes, Plugin ->FunctionTypes, fl->nFunctions * sizeof(cmsUInt32Number));
memmove(fl->ParameterCount, Plugin ->ParameterCount, fl->nFunctions * sizeof(cmsUInt32Number));
// Keep linked list
fl ->Next = ParametricCurves;
ParametricCurves = fl;
// All is ok
return TRUE;
}
// Search in type list, return position or -1 if not found
static
int IsInSet(int Type, _cmsParametricCurvesCollection* c)
{
int i;
for (i=0; i < c ->nFunctions; i++)
if (abs(Type) == c ->FunctionTypes[i]) return i;
return -1;
}
// Search for the collection which contains a specific type
static
_cmsParametricCurvesCollection *GetParametricCurveByType(int Type, int* index)
{
_cmsParametricCurvesCollection* c;
int Position;
for (c = ParametricCurves; c != NULL; c = c ->Next) {
Position = IsInSet(Type, c);
if (Position != -1) {
if (index != NULL)
*index = Position;
return c;
}
}
return NULL;
}
// Low level allocate, which takes care of memory details. nEntries may be zero, and in this case
// no optimation curve is computed. nSegments may also be zero in the inverse case, where only the
// optimization curve is given. Both features simultaneously is an error
static
cmsToneCurve* AllocateToneCurveStruct(cmsContext ContextID, cmsInt32Number nEntries,
cmsInt32Number nSegments, const cmsCurveSegment* Segments,
const cmsUInt16Number* Values)
{
cmsToneCurve* p;
int i;
// We allow huge tables, which are then restricted for smoothing operations
if (nEntries > 65530 || nEntries < 0) {
cmsSignalError(ContextID, cmsERROR_RANGE, "Couldn't create tone curve of more than 65530 entries");
return NULL;
}
if (nEntries <= 0 && nSegments <= 0) {
cmsSignalError(ContextID, cmsERROR_RANGE, "Couldn't create tone curve with zero segments and no table");
return NULL;
}
// Allocate all required pointers, etc.
p = (cmsToneCurve*) _cmsMallocZero(ContextID, sizeof(cmsToneCurve));
if (!p) return NULL;
// In this case, there are no segments
if (nSegments <= 0) {
p ->Segments = NULL;
p ->Evals = NULL;
}
else {
p ->Segments = (cmsCurveSegment*) _cmsCalloc(ContextID, nSegments, sizeof(cmsCurveSegment));
if (p ->Segments == NULL) goto Error;
p ->Evals = (cmsParametricCurveEvaluator*) _cmsCalloc(ContextID, nSegments, sizeof(cmsParametricCurveEvaluator));
if (p ->Evals == NULL) goto Error;
}
p -> nSegments = nSegments;
// This 16-bit table contains a limited precision representation of the whole curve and is kept for
// increasing xput on certain operations.
if (nEntries <= 0) {
p ->Table16 = NULL;
}
else {
p ->Table16 = (cmsUInt16Number*) _cmsCalloc(ContextID, nEntries, sizeof(cmsUInt16Number));
if (p ->Table16 == NULL) goto Error;
}
p -> nEntries = nEntries;
// Initialize members if requested
if (Values != NULL && (nEntries > 0)) {
for (i=0; i < nEntries; i++)
p ->Table16[i] = Values[i];
}
// Initialize the segments stuff. The evaluator for each segment is located and a pointer to it
// is placed in advance to maximize performance.
if (Segments != NULL && (nSegments > 0)) {
_cmsParametricCurvesCollection *c;
p ->SegInterp = (cmsInterpParams**) _cmsCalloc(ContextID, nSegments, sizeof(cmsInterpParams*));
if (p ->SegInterp == NULL) goto Error;
for (i=0; i< nSegments; i++) {
// Type 0 is a special marker for table-based curves
if (Segments[i].Type == 0)
p ->SegInterp[i] = _cmsComputeInterpParams(ContextID, Segments[i].nGridPoints, 1, 1, NULL, CMS_LERP_FLAGS_FLOAT);
memmove(&p ->Segments[i], &Segments[i], sizeof(cmsCurveSegment));
if (Segments[i].Type == 0 && Segments[i].SampledPoints != NULL)
p ->Segments[i].SampledPoints = (cmsFloat32Number*) _cmsDupMem(ContextID, Segments[i].SampledPoints, sizeof(cmsFloat32Number) * Segments[i].nGridPoints);
else
p ->Segments[i].SampledPoints = NULL;
c = GetParametricCurveByType(Segments[i].Type, NULL);
if (c != NULL)
p ->Evals[i] = c ->Evaluator;
}
}
p ->InterpParams = _cmsComputeInterpParams(ContextID, p ->nEntries, 1, 1, p->Table16, CMS_LERP_FLAGS_16BITS);
return p;
Error:
if (p -> Segments) _cmsFree(ContextID, p ->Segments);
if (p -> Evals) _cmsFree(ContextID, p -> Evals);
if (p ->Table16) _cmsFree(ContextID, p ->Table16);
_cmsFree(ContextID, p);
return NULL;
}
// Parametric Fn using floating point
static
cmsFloat64Number DefaultEvalParametricFn(cmsInt32Number Type, const cmsFloat64Number Params[], cmsFloat64Number R)
{
cmsFloat64Number e, Val, disc;
switch (Type) {
// X = Y ^ Gamma
case 1:
if (R < 0) {
if (fabs(Params[0] - 1.0) < MATRIX_DET_TOLERANCE)
Val = R;
else
Val = 0;
}
else
Val = pow(R, Params[0]);
break;
// Type 1 Reversed: X = Y ^1/gamma
case -1:
if (R < 0) {
if (fabs(Params[0] - 1.0) < MATRIX_DET_TOLERANCE)
Val = R;
else
Val = 0;
}
else
Val = pow(R, 1/Params[0]);
break;
// CIE 122-1966
// Y = (aX + b)^Gamma | X >= -b/a
// Y = 0 | else
case 2:
disc = -Params[2] / Params[1];
if (R >= disc ) {
e = Params[1]*R + Params[2];
if (e > 0)
Val = pow(e, Params[0]);
else
Val = 0;
}
else
Val = 0;
break;
// Type 2 Reversed
// X = (Y ^1/g - b) / a
case -2:
if (R < 0)
Val = 0;
else
Val = (pow(R, 1.0/Params[0]) - Params[2]) / Params[1];
if (Val < 0)
Val = 0;
break;
// IEC 61966-3
// Y = (aX + b)^Gamma | X <= -b/a
// Y = c | else
case 3:
disc = -Params[2] / Params[1];
if (disc < 0)
disc = 0;
if (R >= disc) {
e = Params[1]*R + Params[2];
if (e > 0)
Val = pow(e, Params[0]) + Params[3];
else
Val = 0;
}
else
Val = Params[3];
break;
// Type 3 reversed
// X=((Y-c)^1/g - b)/a | (Y>=c)
// X=-b/a | (Y<c)
case -3:
if (R >= Params[3]) {
e = R - Params[3];
if (e > 0)
Val = (pow(e, 1/Params[0]) - Params[2]) / Params[1];
else
Val = 0;
}
else {
Val = -Params[2] / Params[1];
}
break;
// IEC 61966-2.1 (sRGB)
// Y = (aX + b)^Gamma | X >= d
// Y = cX | X < d
case 4:
if (R >= Params[4]) {
e = Params[1]*R + Params[2];
if (e > 0)
Val = pow(e, Params[0]);
else
Val = 0;
}
else
Val = R * Params[3];
break;
// Type 4 reversed
// X=((Y^1/g-b)/a) | Y >= (ad+b)^g
// X=Y/c | Y< (ad+b)^g
case -4:
e = Params[1] * Params[4] + Params[2];
if (e < 0)
disc = 0;
else
disc = pow(e, Params[0]);
if (R >= disc) {
Val = (pow(R, 1.0/Params[0]) - Params[2]) / Params[1];
}
else {
Val = R / Params[3];
}
break;
// Y = (aX + b)^Gamma + e | X >= d
// Y = cX + f | X < d
case 5:
if (R >= Params[4]) {
e = Params[1]*R + Params[2];
if (e > 0)
Val = pow(e, Params[0]) + Params[5];
else
Val = 0;
}
else
Val = R*Params[3] + Params[6];
break;
// Reversed type 5
// X=((Y-e)1/g-b)/a | Y >=(ad+b)^g+e), cd+f
// X=(Y-f)/c | else
case -5:
disc = Params[3] * Params[4] + Params[6];
if (R >= disc) {
e = R - Params[5];
if (e < 0)
Val = 0;
else
Val = (pow(e, 1.0/Params[0]) - Params[2]) / Params[1];
}
else {
Val = (R - Params[6]) / Params[3];
}
break;
// Types 6,7,8 comes from segmented curves as described in ICCSpecRevision_02_11_06_Float.pdf
// Type 6 is basically identical to type 5 without d
// Y = (a * X + b) ^ Gamma + c
case 6:
e = Params[1]*R + Params[2];
if (e < 0)
Val = 0;
else
Val = pow(e, Params[0]) + Params[3];
break;
// ((Y - c) ^1/Gamma - b) / a
case -6:
e = R - Params[3];
if (e < 0)
Val = 0;
else
Val = (pow(e, 1.0/Params[0]) - Params[2]) / Params[1];
break;
// Y = a * log (b * X^Gamma + c) + d
case 7:
e = Params[2] * pow(R, Params[0]) + Params[3];
if (e <= 0)
Val = 0;
else
Val = Params[1]*log10(e) + Params[4];
break;
// (Y - d) / a = log(b * X ^Gamma + c)
// pow(10, (Y-d) / a) = b * X ^Gamma + c
// pow((pow(10, (Y-d) / a) - c) / b, 1/g) = X
case -7:
Val = pow((pow(10.0, (R-Params[4]) / Params[1]) - Params[3]) / Params[2], 1.0 / Params[0]);
break;
//Y = a * b^(c*X+d) + e
case 8:
Val = (Params[0] * pow(Params[1], Params[2] * R + Params[3]) + Params[4]);
break;
// Y = (log((y-e) / a) / log(b) - d ) / c
// a=0, b=1, c=2, d=3, e=4,
case -8:
disc = R - Params[4];
if (disc < 0) Val = 0;
else
Val = (log(disc / Params[0]) / log(Params[1]) - Params[3]) / Params[2];
break;
// S-Shaped: (1 - (1-x)^1/g)^1/g
case 108:
Val = pow(1.0 - pow(1 - R, 1/Params[0]), 1/Params[0]);
break;
// y = (1 - (1-x)^1/g)^1/g
// y^g = (1 - (1-x)^1/g)
// 1 - y^g = (1-x)^1/g
// (1 - y^g)^g = 1 - x
// 1 - (1 - y^g)^g
case -108:
Val = 1 - pow(1 - pow(R, Params[0]), Params[0]);
break;
default:
// Unsupported parametric curve. Should never reach here
return 0;
}
return Val;
}
// Evaluate a segmented funtion for a single value. Return -1 if no valid segment found .
// If fn type is 0, perform an interpolation on the table
static
cmsFloat64Number EvalSegmentedFn(const cmsToneCurve *g, cmsFloat64Number R)
{
int i;
for (i = g ->nSegments-1; i >= 0 ; --i) {
// Check for domain
if ((R > g ->Segments[i].x0) && (R <= g ->Segments[i].x1)) {
// Type == 0 means segment is sampled
if (g ->Segments[i].Type == 0) {
cmsFloat32Number R1 = (cmsFloat32Number) (R - g ->Segments[i].x0);
cmsFloat32Number Out;
// Setup the table (TODO: clean that)
g ->SegInterp[i]-> Table = g ->Segments[i].SampledPoints;
g ->SegInterp[i] -> Interpolation.LerpFloat(&R1, &Out, g ->SegInterp[i]);
return Out;
}
else
return g ->Evals[i](g->Segments[i].Type, g ->Segments[i].Params, R);
}
}
return MINUS_INF;
}
// Access to estimated low-res table
cmsUInt32Number CMSEXPORT cmsGetToneCurveEstimatedTableEntries(const cmsToneCurve* t)
{
_cmsAssert(t != NULL);
return t ->nEntries;
}
const cmsUInt16Number* CMSEXPORT cmsGetToneCurveEstimatedTable(const cmsToneCurve* t)
{
_cmsAssert(t != NULL);
return t ->Table16;
}
// Create an empty gamma curve, by using tables. This specifies only the limited-precision part, and leaves the
// floating point description empty.
cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurve16(cmsContext ContextID, cmsInt32Number nEntries, const cmsUInt16Number Values[])
{
return AllocateToneCurveStruct(ContextID, nEntries, 0, NULL, Values);
}
static
int EntriesByGamma(cmsFloat64Number Gamma)
{
if (fabs(Gamma - 1.0) < 0.001) return 2;
return 4096;
}
// Create a segmented gamma, fill the table
cmsToneCurve* CMSEXPORT cmsBuildSegmentedToneCurve(cmsContext ContextID,
cmsInt32Number nSegments, const cmsCurveSegment Segments[])
{
int i;
cmsFloat64Number R, Val;
cmsToneCurve* g;
int nGridPoints = 4096;
_cmsAssert(Segments != NULL);
// Optimizatin for identity curves.
if (nSegments == 1 && Segments[0].Type == 1) {
nGridPoints = EntriesByGamma(Segments[0].Params[0]);
}
g = AllocateToneCurveStruct(ContextID, nGridPoints, nSegments, Segments, NULL);
if (g == NULL) return NULL;
// Once we have the floating point version, we can approximate a 16 bit table of 4096 entries
// for performance reasons. This table would normally not be used except on 8/16 bits transforms.
for (i=0; i < nGridPoints; i++) {
R = (cmsFloat64Number) i / (nGridPoints-1);
Val = EvalSegmentedFn(g, R);
// Round and saturate
g ->Table16[i] = _cmsQuickSaturateWord(Val * 65535.0);
}
return g;
}
// Use a segmented curve to store the floating point table
cmsToneCurve* CMSEXPORT cmsBuildTabulatedToneCurveFloat(cmsContext ContextID, cmsUInt32Number nEntries, const cmsFloat32Number values[])
{
cmsCurveSegment Seg[2];
// Initialize segmented curve part up to 0
Seg[0].x0 = -1;
Seg[0].x1 = 0;
Seg[0].Type = 6;
Seg[0].Params[0] = 1;
Seg[0].Params[1] = 0;
Seg[0].Params[2] = 0;
Seg[0].Params[3] = 0;
Seg[0].Params[4] = 0;
// From zero to any
Seg[1].x0 = 0;
Seg[1].x1 = 1.0;
Seg[1].Type = 0;
Seg[1].nGridPoints = nEntries;
Seg[1].SampledPoints = (cmsFloat32Number*) values;
return cmsBuildSegmentedToneCurve(ContextID, 2, Seg);
}
// Parametric curves
//
// Parameters goes as: Curve, a, b, c, d, e, f
// Type is the ICC type +1
// if type is negative, then the curve is analyticaly inverted
cmsToneCurve* CMSEXPORT cmsBuildParametricToneCurve(cmsContext ContextID, cmsInt32Number Type, const cmsFloat64Number Params[])
{
cmsCurveSegment Seg0;
int Pos = 0;
cmsUInt32Number size;
_cmsParametricCurvesCollection* c = GetParametricCurveByType(Type, &Pos);
_cmsAssert(Params != NULL);
if (c == NULL) {
cmsSignalError(ContextID, cmsERROR_UNKNOWN_EXTENSION, "Invalid parametric curve type %d", Type);
return NULL;
}
memset(&Seg0, 0, sizeof(Seg0));
Seg0.x0 = MINUS_INF;
Seg0.x1 = PLUS_INF;
Seg0.Type = Type;
size = c->ParameterCount[Pos] * sizeof(cmsFloat64Number);
memmove(Seg0.Params, Params, size);
return cmsBuildSegmentedToneCurve(ContextID, 1, &Seg0);
}
// Build a gamma table based on gamma constant
cmsToneCurve* CMSEXPORT cmsBuildGamma(cmsContext ContextID, cmsFloat64Number Gamma)
{
return cmsBuildParametricToneCurve(ContextID, 1, &Gamma);
}
// Free all memory taken by the gamma curve
void CMSEXPORT cmsFreeToneCurve(cmsToneCurve* Curve)
{
cmsContext ContextID;
if (Curve == NULL) return;
ContextID = Curve ->InterpParams->ContextID;
_cmsFreeInterpParams(Curve ->InterpParams);
if (Curve -> Table16)
_cmsFree(ContextID, Curve ->Table16);
if (Curve ->Segments) {
cmsUInt32Number i;
for (i=0; i < Curve ->nSegments; i++) {
if (Curve ->Segments[i].SampledPoints) {
_cmsFree(ContextID, Curve ->Segments[i].SampledPoints);
}
if (Curve ->SegInterp[i] != 0)
_cmsFreeInterpParams(Curve->SegInterp[i]);
}
_cmsFree(ContextID, Curve ->Segments);
_cmsFree(ContextID, Curve ->SegInterp);
}
if (Curve -> Evals)
_cmsFree(ContextID, Curve -> Evals);
if (Curve) _cmsFree(ContextID, Curve);
}
// Utility function, free 3 gamma tables
void CMSEXPORT cmsFreeToneCurveTriple(cmsToneCurve* Curve[3])
{
_cmsAssert(Curve != NULL);
if (Curve[0] != NULL) cmsFreeToneCurve(Curve[0]);
if (Curve[1] != NULL) cmsFreeToneCurve(Curve[1]);
if (Curve[2] != NULL) cmsFreeToneCurve(Curve[2]);
Curve[0] = Curve[1] = Curve[2] = NULL;
}
// Duplicate a gamma table
cmsToneCurve* CMSEXPORT cmsDupToneCurve(const cmsToneCurve* In)
{
if (In == NULL) return NULL;
return AllocateToneCurveStruct(In ->InterpParams ->ContextID, In ->nEntries, In ->nSegments, In ->Segments, In ->Table16);
}
// Joins two curves for X and Y. Curves should be monotonic.
// We want to get
//
// y = Y^-1(X(t))
//
cmsToneCurve* CMSEXPORT cmsJoinToneCurve(cmsContext ContextID,
const cmsToneCurve* X,
const cmsToneCurve* Y, cmsUInt32Number nResultingPoints)
{
cmsToneCurve* out = NULL;
cmsToneCurve* Yreversed = NULL;
cmsFloat32Number t, x;
cmsFloat32Number* Res = NULL;
cmsUInt32Number i;
_cmsAssert(X != NULL);
_cmsAssert(Y != NULL);
Yreversed = cmsReverseToneCurveEx(nResultingPoints, Y);
if (Yreversed == NULL) goto Error;
Res = (cmsFloat32Number*) _cmsCalloc(ContextID, nResultingPoints, sizeof(cmsFloat32Number));
if (Res == NULL) goto Error;
//Iterate
for (i=0; i < nResultingPoints; i++) {
t = (cmsFloat32Number) i / (nResultingPoints-1);
x = cmsEvalToneCurveFloat(X, t);
Res[i] = cmsEvalToneCurveFloat(Yreversed, x);
}
// Allocate space for output
out = cmsBuildTabulatedToneCurveFloat(ContextID, nResultingPoints, Res);
Error:
if (Res != NULL) _cmsFree(ContextID, Res);
if (Yreversed != NULL) cmsFreeToneCurve(Yreversed);
return out;
}
// Get the surrounding nodes. This is tricky on non-monotonic tables
static
int GetInterval(cmsFloat64Number In, const cmsUInt16Number LutTable[], const struct _cms_interp_struc* p)
{
int i;
int y0, y1;
// A 1 point table is not allowed
if (p -> Domain[0] < 1) return -1;
// Let's see if ascending or descending.
if (LutTable[0] < LutTable[p ->Domain[0]]) {
// Table is overall ascending
for (i=p->Domain[0]-1; i >=0; --i) {
y0 = LutTable[i];
y1 = LutTable[i+1];
if (y0 <= y1) { // Increasing
if (In >= y0 && In <= y1) return i;
}
else
if (y1 < y0) { // Decreasing
if (In >= y1 && In <= y0) return i;
}
}
}
else {
// Table is overall descending
for (i=0; i < (int) p -> Domain[0]; i++) {
y0 = LutTable[i];
y1 = LutTable[i+1];
if (y0 <= y1) { // Increasing
if (In >= y0 && In <= y1) return i;
}
else
if (y1 < y0) { // Decreasing
if (In >= y1 && In <= y0) return i;
}
}
}
return -1;
}
// Reverse a gamma table
cmsToneCurve* CMSEXPORT cmsReverseToneCurveEx(cmsInt32Number nResultSamples, const cmsToneCurve* InCurve)
{
cmsToneCurve *out;
cmsFloat64Number a = 0, b = 0, y, x1, y1, x2, y2;
int i, j;
int Ascending;
_cmsAssert(InCurve != NULL);
// Try to reverse it analytically whatever possible
if (InCurve ->nSegments == 1 && InCurve ->Segments[0].Type > 0 && InCurve -> Segments[0].Type <= 5) {
return cmsBuildParametricToneCurve(InCurve ->InterpParams->ContextID,
-(InCurve -> Segments[0].Type),
InCurve -> Segments[0].Params);
}
// Nope, reverse the table.
out = cmsBuildTabulatedToneCurve16(InCurve ->InterpParams->ContextID, nResultSamples, NULL);
if (out == NULL)
return NULL;
// We want to know if this is an ascending or descending table
Ascending = !cmsIsToneCurveDescending(InCurve);
// Iterate across Y axis
for (i=0; i < nResultSamples; i++) {
y = (cmsFloat64Number) i * 65535.0 / (nResultSamples - 1);
// Find interval in which y is within.
j = GetInterval(y, InCurve->Table16, InCurve->InterpParams);
if (j >= 0) {
// Get limits of interval
x1 = InCurve ->Table16[j];
x2 = InCurve ->Table16[j+1];
y1 = (cmsFloat64Number) (j * 65535.0) / (InCurve ->nEntries - 1);
y2 = (cmsFloat64Number) ((j+1) * 65535.0 ) / (InCurve ->nEntries - 1);
// If collapsed, then use any
if (x1 == x2) {
out ->Table16[i] = _cmsQuickSaturateWord(Ascending ? y2 : y1);
continue;
} else {
// Interpolate
a = (y2 - y1) / (x2 - x1);
b = y2 - a * x2;
}
}
out ->Table16[i] = _cmsQuickSaturateWord(a* y + b);
}
return out;
}
// Reverse a gamma table
cmsToneCurve* CMSEXPORT cmsReverseToneCurve(const cmsToneCurve* InGamma)
{
_cmsAssert(InGamma != NULL);
return cmsReverseToneCurveEx(4096, InGamma);
}
// From: Eilers, P.H.C. (1994) Smoothing and interpolation with finite
// differences. in: Graphic Gems IV, Heckbert, P.S. (ed.), Academic press.
//
// Smoothing and interpolation with second differences.
//
// Input: weights (w), data (y): vector from 1 to m.
// Input: smoothing parameter (lambda), length (m).
// Output: smoothed vector (z): vector from 1 to m.
static
cmsBool smooth2(cmsContext ContextID, cmsFloat32Number w[], cmsFloat32Number y[], cmsFloat32Number z[], cmsFloat32Number lambda, int m)
{
int i, i1, i2;
cmsFloat32Number *c, *d, *e;
cmsBool st;
c = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
d = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
e = (cmsFloat32Number*) _cmsCalloc(ContextID, MAX_NODES_IN_CURVE, sizeof(cmsFloat32Number));
if (c != NULL && d != NULL && e != NULL) {
d[1] = w[1] + lambda;
c[1] = -2 * lambda / d[1];
e[1] = lambda /d[1];
z[1] = w[1] * y[1];
d[2] = w[2] + 5 * lambda - d[1] * c[1] * c[1];
c[2] = (-4 * lambda - d[1] * c[1] * e[1]) / d[2];
e[2] = lambda / d[2];
z[2] = w[2] * y[2] - c[1] * z[1];
for (i = 3; i < m - 1; i++) {
i1 = i - 1; i2 = i - 2;
d[i]= w[i] + 6 * lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
c[i] = (-4 * lambda -d[i1] * c[i1] * e[i1])/ d[i];
e[i] = lambda / d[i];
z[i] = w[i] * y[i] - c[i1] * z[i1] - e[i2] * z[i2];
}
i1 = m - 2; i2 = m - 3;
d[m - 1] = w[m - 1] + 5 * lambda -c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
c[m - 1] = (-2 * lambda - d[i1] * c[i1] * e[i1]) / d[m - 1];
z[m - 1] = w[m - 1] * y[m - 1] - c[i1] * z[i1] - e[i2] * z[i2];
i1 = m - 1; i2 = m - 2;
d[m] = w[m] + lambda - c[i1] * c[i1] * d[i1] - e[i2] * e[i2] * d[i2];
z[m] = (w[m] * y[m] - c[i1] * z[i1] - e[i2] * z[i2]) / d[m];
z[m - 1] = z[m - 1] / d[m - 1] - c[m - 1] * z[m];
for (i = m - 2; 1<= i; i--)
z[i] = z[i] / d[i] - c[i] * z[i + 1] - e[i] * z[i + 2];
st = TRUE;
}
else st = FALSE;
if (c != NULL) _cmsFree(ContextID, c);
if (d != NULL) _cmsFree(ContextID, d);
if (e != NULL) _cmsFree(ContextID, e);
return st;
}
// Smooths a curve sampled at regular intervals.
cmsBool CMSEXPORT cmsSmoothToneCurve(cmsToneCurve* Tab, cmsFloat64Number lambda)
{
cmsFloat32Number w[MAX_NODES_IN_CURVE], y[MAX_NODES_IN_CURVE], z[MAX_NODES_IN_CURVE];
int i, nItems, Zeros, Poles;
if (Tab == NULL) return FALSE;
if (cmsIsToneCurveLinear(Tab)) return FALSE; // Nothing to do
nItems = Tab -> nEntries;
if (nItems >= MAX_NODES_IN_CURVE) {
cmsSignalError(Tab ->InterpParams->ContextID, cmsERROR_RANGE, "cmsSmoothToneCurve: too many points.");
return FALSE;
}
memset(w, 0, nItems * sizeof(cmsFloat32Number));
memset(y, 0, nItems * sizeof(cmsFloat32Number));
memset(z, 0, nItems * sizeof(cmsFloat32Number));
for (i=0; i < nItems; i++)
{
y[i+1] = (cmsFloat32Number) Tab -> Table16[i];
w[i+1] = 1.0;
}
if (!smooth2(Tab ->InterpParams->ContextID, w, y, z, (cmsFloat32Number) lambda, nItems)) return FALSE;
// Do some reality - checking...
Zeros = Poles = 0;
for (i=nItems; i > 1; --i) {
if (z[i] == 0.) Zeros++;
if (z[i] >= 65535.) Poles++;
if (z[i] < z[i-1]) return FALSE; // Non-Monotonic
}
if (Zeros > (nItems / 3)) return FALSE; // Degenerated, mostly zeros
if (Poles > (nItems / 3)) return FALSE; // Degenerated, mostly poles
// Seems ok
for (i=0; i < nItems; i++) {
// Clamp to cmsUInt16Number
Tab -> Table16[i] = _cmsQuickSaturateWord(z[i+1]);
}
return TRUE;
}
// Is a table linear? Do not use parametric since we cannot guarantee some weird parameters resulting
// in a linear table. This way assures it is linear in 12 bits, which should be enought in most cases.
cmsBool CMSEXPORT cmsIsToneCurveLinear(const cmsToneCurve* Curve)
{
cmsUInt32Number i;
int diff;
_cmsAssert(Curve != NULL);
for (i=0; i < Curve ->nEntries; i++) {
diff = abs((int) Curve->Table16[i] - (int) _cmsQuantizeVal(i, Curve ->nEntries));
if (diff > 0x0f)
return FALSE;
}
return TRUE;
}
// Same, but for monotonicity
cmsBool CMSEXPORT cmsIsToneCurveMonotonic(const cmsToneCurve* t)
{
int n;
int i, last;
cmsBool lDescending;
_cmsAssert(t != NULL);
// Degenerated curves are monotonic? Ok, let's pass them
n = t ->nEntries;
if (n < 2) return TRUE;
// Curve direction
lDescending = cmsIsToneCurveDescending(t);
if (lDescending) {
last = t ->Table16[0];
for (i = 1; i < n; i++) {
if (t ->Table16[i] - last > 2) // We allow some ripple
return FALSE;
else
last = t ->Table16[i];
}
}
else {
last = t ->Table16[n-1];
for (i = n-2; i >= 0; --i) {
if (t ->Table16[i] - last > 2)
return FALSE;
else
last = t ->Table16[i];
}
}
return TRUE;
}
// Same, but for descending tables
cmsBool CMSEXPORT cmsIsToneCurveDescending(const cmsToneCurve* t)
{
_cmsAssert(t != NULL);
return t ->Table16[0] > t ->Table16[t ->nEntries-1];
}
// Another info fn: is out gamma table multisegment?
cmsBool CMSEXPORT cmsIsToneCurveMultisegment(const cmsToneCurve* t)
{
_cmsAssert(t != NULL);
return t -> nSegments > 1;
}
cmsInt32Number CMSEXPORT cmsGetToneCurveParametricType(const cmsToneCurve* t)
{
_cmsAssert(t != NULL);
if (t -> nSegments != 1) return 0;
return t ->Segments[0].Type;
}
// We need accuracy this time
cmsFloat32Number CMSEXPORT cmsEvalToneCurveFloat(const cmsToneCurve* Curve, cmsFloat32Number v)
{
_cmsAssert(Curve != NULL);
// Check for 16 bits table. If so, this is a limited-precision tone curve
if (Curve ->nSegments == 0) {
cmsUInt16Number In, Out;
In = (cmsUInt16Number) _cmsQuickSaturateWord(v * 65535.0);
Out = cmsEvalToneCurve16(Curve, In);
return (cmsFloat32Number) (Out / 65535.0);
}
return (cmsFloat32Number) EvalSegmentedFn(Curve, v);
}
// We need xput over here
cmsUInt16Number CMSEXPORT cmsEvalToneCurve16(const cmsToneCurve* Curve, cmsUInt16Number v)
{
cmsUInt16Number out;
_cmsAssert(Curve != NULL);
Curve ->InterpParams ->Interpolation.Lerp16(&v, &out, Curve ->InterpParams);
return out;
}
// Least squares fitting.
// A mathematical procedure for finding the best-fitting curve to a given set of points by
// minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve.
// The sum of the squares of the offsets is used instead of the offset absolute values because
// this allows the residuals to be treated as a continuous differentiable quantity.
//
// y = f(x) = x ^ g
//
// R = (yi - (xi^g))
// R2 = (yi - (xi^g))2
// SUM R2 = SUM (yi - (xi^g))2
//
// dR2/dg = -2 SUM x^g log(x)(y - x^g)
// solving for dR2/dg = 0
//
// g = 1/n * SUM(log(y) / log(x))
cmsFloat64Number CMSEXPORT cmsEstimateGamma(const cmsToneCurve* t, cmsFloat64Number Precision)
{
cmsFloat64Number gamma, sum, sum2;
cmsFloat64Number n, x, y, Std;
cmsUInt32Number i;
_cmsAssert(t != NULL);
sum = sum2 = n = 0;
// Excluding endpoints
for (i=1; i < (MAX_NODES_IN_CURVE-1); i++) {
x = (cmsFloat64Number) i / (MAX_NODES_IN_CURVE-1);
y = (cmsFloat64Number) cmsEvalToneCurveFloat(t, (cmsFloat32Number) x);
// Avoid 7% on lower part to prevent
// artifacts due to linear ramps
if (y > 0. && y < 1. && x > 0.07) {
gamma = log(y) / log(x);
sum += gamma;
sum2 += gamma * gamma;
n++;
}
}
// Take a look on SD to see if gamma isn't exponential at all
Std = sqrt((n * sum2 - sum * sum) / (n*(n-1)));
if (Std > Precision)
return -1.0;
return (sum / n); // The mean
}