/
transform.js
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/
transform.js
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// __BEGIN_LICENSE__
// Copyright (C) 2008-2010 United States Government as represented by
// the Administrator of the National Aeronautics and Space Administration.
// All Rights Reserved.
// __END_LICENSE__
var geocamTiePoint = window.geocamTiePoint || {};
geocamTiePoint.transform = {};
$(function($) {
function matrixFromNestedList(nestedList) {
var height = nestedList.length;
var width = nestedList[0].length;
return new Matrix(width, height, nestedList);
}
function columnVectorFromPt(pt) {
return new Matrix(1, 3,
[[pt[0]],
[pt[1]],
[1]]);
}
function quadraticColumnVectorFromPt(pt) {
return new Matrix(1, 5,
[[pt[0] * pt[0]],
[pt[1] * pt[1]],
[pt[0]],
[pt[1]],
[1]]);
}
function ptFromColumnVector(v) {
var z = v.values[2][0];
return [v.values[0][0] / z,
v.values[1][0] / z];
}
function forwardPoints(tform, fromPts) {
var toPts = new Matrix(fromPts.w, fromPts.h);
var n = fromPts.w;
for (var i = 0; i < n; i++) {
var x = fromPts.values[0][i];
var y = fromPts.values[1][i];
var out = tform.forward([x, y]);
toPts.values[0][i] = out[0];
toPts.values[1][i] = out[1];
}
return toPts;
}
function linearLeastSquares(V, U) {
var tmp = U.transpose().multiply(V);
return U.transpose().multiply(U).invert().multiply(tmp);
}
function leastSquares(y, f, x0) {
var result = geocamTiePoint.optimize.lm(y, f, x0);
return result[0];
}
function splitPoints(points) {
var n = points.length;
var toPts = new Matrix(n, 2);
var fromPts = new Matrix(n, 2);
for (var i = 0; i < n; i++) {
toPts.values[0][i] = points[i][0];
toPts.values[1][i] = points[i][1];
fromPts.values[0][i] = points[i][2];
fromPts.values[1][i] = points[i][3];
}
return [toPts, fromPts];
}
function vectorBetweenFirstTwoPoints(pts) {
var x0 = pts.values[0][0];
var y0 = pts.values[1][0];
var x1 = pts.values[0][1];
var y1 = pts.values[1][1];
return [x1 - x0, y1 - y0];
}
function norm(v) {
return Math.sqrt(v[0] * v[0] +
v[1] * v[1]);
}
function angle(v) {
return Math.atan2(v[1], v[0]);
}
/**********************************************************************
* Transform
**********************************************************************/
function Transform() {}
Transform.fit = function(cls, toPts, fromPts) {
var params0 = cls.getInitParams(toPts, fromPts);
// console.log('fit: params0: ' + JSON.stringify(params0));
var params = (leastSquares
(toPts.flatten(),
function(params) {
return (forwardPoints(cls.fromParams(params),
fromPts)
.flatten());
},
params0));
//console.log('fit: params: ' + JSON.stringify(params));
return params;
};
/**********************************************************************
* LinearTransform
**********************************************************************/
function LinearTransform(matrix) {
this.matrix = matrix;
}
LinearTransform.prototype = $.extend(true,
{},
Transform.prototype);
LinearTransform.prototype.forward = function(pt) {
var u = columnVectorFromPt(pt);
var v = this.matrix.multiply(u);
return ptFromColumnVector(v);
};
LinearTransform.prototype.toDict = function() {
return {
type: 'projective',
matrix: this.matrix.values
};
};
/**********************************************************************
* AffineTransform
**********************************************************************/
function AffineTransform(matrix) {
this.matrix = matrix;
}
AffineTransform.prototype = $.extend(true,
{},
LinearTransform.prototype);
AffineTransform.fit = function(cls, toPts, fromPts) {
var n = toPts.w;
var V = new Matrix(1, 2 * n);
var U = new Matrix(6, 2 * n);
for (var i = 0; i < n; i++) {
V.values[2 * i][0] = toPts.values[0][i];
V.values[2 * i + 1][0] = toPts.values[1][i];
U.values[2 * i][0] = fromPts.values[0][i];
U.values[2 * i][1] = fromPts.values[1][i];
U.values[2 * i][2] = 1;
U.values[2 * i + 1][3] = fromPts.values[0][i];
U.values[2 * i + 1][4] = fromPts.values[1][i];
U.values[2 * i + 1][5] = 1;
}
var p = linearLeastSquares(V, U);
return [p.values[0][0],
p.values[1][0],
p.values[2][0],
p.values[3][0],
p.values[4][0],
p.values[5][0]];
};
AffineTransform.fromParams = function(p) {
var matrix = new Matrix(3, 3,
[[p[0], p[1], p[2]],
[p[3], p[4], p[5]],
[0, 0, 1]]);
return new AffineTransform(matrix);
};
/**********************************************************************
* RotateScaleTranslateTransform
**********************************************************************/
function RotateScaleTranslateTransform(matrix) {
this.matrix = matrix;
}
(RotateScaleTranslateTransform.prototype =
$.extend(true,
{},
LinearTransform.prototype));
RotateScaleTranslateTransform.fromDict = function(transformDict) {
var matrix = matrixFromNestedList(transformDict.matrix);
return new RotateScaleTranslateTransform(matrix);
};
RotateScaleTranslateTransform.fromParams = function(p) {
var tx = p[0];
var ty = p[1];
var scale = p[2];
var theta = p[3];
var translateMatrix = new Matrix(3, 3,
[[1, 0, tx],
[0, 1, ty],
[0, 0, 1]]);
var scaleMatrix = new Matrix(3, 3,
[[scale, 0, 0],
[0, -scale, 0],
[0, 0, 1]]);
var rotateMatrix = new Matrix(3, 3,
[[Math.cos(theta), -Math.sin(theta), 0],
[Math.sin(theta), Math.cos(theta), 0],
[0, 0, 1]]);
var matrix = (translateMatrix
.multiply(scaleMatrix)
.multiply(rotateMatrix));
return new RotateScaleTranslateTransform(matrix);
};
RotateScaleTranslateTransform.getInitParams = function(toPts, fromPts) {
var centroidDiff = toPts.meanColumn().subtract(fromPts.meanColumn());
var tx = centroidDiff.values[0][0];
var ty = centroidDiff.values[1][0];
var toVec = vectorBetweenFirstTwoPoints(toPts);
var fromVec = vectorBetweenFirstTwoPoints(fromPts);
var scale = norm(toVec) / norm(fromVec);
var theta = angle(toVec) - angle(fromVec);
return [tx, ty, scale, theta];
};
RotateScaleTranslateTransform.fit = Transform.fit;
/**********************************************************************
* ProjectiveTransform
**********************************************************************/
function ProjectiveTransform(matrix) {
this.matrix = matrix;
}
ProjectiveTransform.prototype = $.extend(true,
{},
LinearTransform.prototype);
ProjectiveTransform.fromDict = function(transformDict) {
var matrix = matrixFromNestedList(transformDict.matrix);
return new ProjectiveTransform(matrix);
};
ProjectiveTransform.fromParams = function(p) {
var matrix = new Matrix(3, 3,
[[p[0], p[1], p[2]],
[p[3], p[4], p[5]],
[p[6], p[7], 1]]);
return new ProjectiveTransform(matrix);
};
ProjectiveTransform.getInitParams = function(toPts, fromPts) {
var p = AffineTransform.fit(AffineTransform, toPts, fromPts);
return p.concat([0, 0]);
};
ProjectiveTransform.fit = Transform.fit;
/**********************************************************************
* QuadraticTransform
**********************************************************************/
function QuadraticTransform(matrix) {
this.matrix = matrix;
}
QuadraticTransform.prototype = $.extend(true,
{},
Transform.prototype);
QuadraticTransform.fromDict = function(transformDict) {
var matrix = matrixFromNestedList(transformDict.matrix);
return new QuadraticTransform(matrix);
};
QuadraticTransform.fromParams = function(p) {
var matrix = new Matrix(5, 3,
[[p[0], p[1], p[2], p[3], p[4]],
[p[5], p[6], p[7], p[8], p[9]],
[0, 0, p[10], p[11], 1]]);
return new QuadraticTransform(matrix);
};
QuadraticTransform.getInitParams = function(toPts, fromPts) {
var p = AffineTransform.fit(AffineTransform, toPts, fromPts);
return [0, 0, p[0], p[1], p[2],
0, 0, p[3], p[4], p[5],
0, 0];
};
QuadraticTransform.fit = Transform.fit;
QuadraticTransform.prototype.forward = function(pt) {
var u = quadraticColumnVectorFromPt(pt);
var v = this.matrix.multiply(u);
return ptFromColumnVector(v);
};
QuadraticTransform.prototype.toDict = function() {
return {
type: 'quadratic',
matrix: this.matrix.values
};
};
/**********************************************************************
* QuadraticTransform2
**********************************************************************/
/* QuadraticTransform2 is similar to QuadraticTransform but modified
* slightly to make it easy to invert analytically (see //
* transform.py). The modification introduces some 4th and 6th order
* terms that should not make much difference in practice.
*
* In order to improve numerical stability when fitting tie points,
* the forward transfrom output is rescaled by a factor of SCALE at
* the last step. Thus the entries in the matrix will be much
* smaller than for the other Transform types. */
function QuadraticTransform2(matrix, quadraticTerms) {
this.matrix = matrix;
this.quadraticTerms = quadraticTerms;
}
QuadraticTransform2.prototype = $.extend(true,
{},
Transform.prototype);
QuadraticTransform2.fromDict = function(transformDict) {
var matrix = matrixFromNestedList(transformDict.matrix);
return new QuadraticTransform2(matrix,
transformDict.quadraticTerms);
};
QuadraticTransform2.fromParams = function(p) {
var matrix = new Matrix(3, 3,
[[p[0], p[1], p[2]],
[p[3], p[4], p[5]],
[p[6], p[7], 1]]);
var quadraticTerms = [p[8], p[9], p[10], p[11]];
return new QuadraticTransform2(matrix, quadraticTerms);
};
var SCALE = 1e+7;
QuadraticTransform2.getInitParams = function(toPts, fromPts) {
// pre-conditioning by SCALE improves numerical stability
var toPtsConditioned = toPts.multiply(1.0 / SCALE);
var p = AffineTransform.fit(AffineTransform, toPtsConditioned, fromPts);
return p.concat([0, 0, 0, 0, 0, 0]);
};
QuadraticTransform2.fit = Transform.fit;
QuadraticTransform2.prototype.forward = function(pt) {
var u = columnVectorFromPt(pt);
var v0 = this.matrix.multiply(u);
var v1 = ptFromColumnVector(v0);
var x = v1[0];
var y = v1[1];
var a = this.quadraticTerms[0];
var b = this.quadraticTerms[1];
var c = this.quadraticTerms[2];
var d = this.quadraticTerms[3];
var p = x + a * x * x;
var q = y + b * y * y;
var r = p + c * q * q;
var s = q + d * r * r;
// correct for pre-conditioning
r = r * SCALE;
s = s * SCALE;
return [r, s];
};
QuadraticTransform2.prototype.toDict = function() {
return {
type: 'quadratic2',
matrix: this.matrix.values,
quadraticTerms: this.quadraticTerms
};
};
/**********************************************************************
* top-level functions
**********************************************************************/
function getTransformClass(n) {
if (n < 2) {
throw 'not enough tie points';
} else if (n == 2) {
return RotateScaleTranslateTransform;
} else if (n == 3) {
return AffineTransform;
} else if (n < 7) {
return ProjectiveTransform;
} else {
return QuadraticTransform2;
}
}
function getTransform0(toPts, fromPts) {
var n = toPts.w;
var cls = getTransformClass(n);
var params = cls.fit(cls, toPts, fromPts);
return cls.fromParams(params);
}
function getTransform(points) {
var s = splitPoints(points);
var toPts = s[0];
var fromPts = s[1];
return getTransform0(toPts, fromPts);
}
function deserializeTransform(transformJSON) {
var classmap = {
'projective': ProjectiveTransform,
'quadratic': QuadraticTransform,
'quadratic2': QuadraticTransform2
};
if (! transformJSON.type in classmap) {
throw 'Unexpected transform type';
}
var transformClass = classmap[transformJSON.type];
if (transformClass === QuadraticTransform2) {
return new transformClass(matrixFromNestedList
(transformJSON.matrix),
transformJSON.quadraticTerms);
} else {
return new transformClass(matrixFromNestedList
(transformJSON.matrix));
}
}
/**********************************************************************
* exports
**********************************************************************/
var ns = geocamTiePoint.transform;
ns.getTransform = getTransform;
ns.splitPoints = splitPoints;
ns.forwardPoints = forwardPoints;
ns.deserializeTransform = deserializeTransform;
});