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import { BucketQueue } from '../BucketQueue';
const { isEqual } = utilities;
const MAX_UINT32 = 4294967295;
const TWO_THIRD_PI = 2 / (3 * Math.PI);
/**
* Scissors
*
* Ref: Eric N. Mortensen, William A. Barrett, Interactive Segmentation with
* Intelligent Scissors, Graphical Models and Image Processing, Volume 60,
* Issue 5, September 1998, Pages 349-384, ISSN 1077-3169,
* DOI: 10.1006/gmip.1998.0480.
*
* {@link http://www.sciencedirect.com/science/article/B6WG4-45JB8WN-9/2/6fe59d8089fd1892c2bfb82283065579}
*
* Implementation based on MIT licensed code at:
* {@link http://code.google.com/p/livewire-javascript/}
*/
export class LivewireScissors {
private searchGranularityBits: number;
private searchGranularity: number;
/** Width of the image */
public readonly width: number;
/** Height of the image */
public readonly height: number;
/** Grayscale image */
private grayscalePixelData: Types.PixelDataTypedArray;
// Laplace zero-crossings (either 0 or 1).
private laplace: Float32Array;
/** Gradient vector magnitude for each pixel */
private gradMagnitude: Float32Array;
/** Gradient of each pixel in the x-direction */
private gradXNew: Float32Array;
/** Gradient of each pixel in the y-direction */
private gradYNew: Float32Array;
/** Dijkstra - start point */
private startPoint: Types.Point2;
/** Dijkstra - store the state of a pixel (visited/unvisited) */
private visited: boolean[];
/** Dijkstra - map a point to its parent along the shortest path to root (start point) */
private parents: Uint32Array;
/** Dijkstra - store the cost to go from the start point to each node */
private costs: Float32Array;
/** Dijkstra - BucketQueue to sort items by priority */
private priorityQueueNew: BucketQueue<number>;
constructor(
grayscalePixelData: Types.PixelDataTypedArray,
width: number,
height: number
) {
const numPixels = grayscalePixelData.length;
this.searchGranularityBits = 8; // Bits of resolution for BucketQueue.
this.searchGranularity = 1 << this.searchGranularityBits; //bits.
this.width = width;
this.height = height;
this.grayscalePixelData = grayscalePixelData;
this.laplace = null;
this.gradXNew = null;
this.gradYNew = null;
this.laplace = this._computeLaplace();
this.gradMagnitude = this._computeGradient();
this.gradXNew = this._computeGradientX();
this.gradYNew = this._computeGradientY();
this.visited = new Array(numPixels);
this.parents = new Uint32Array(numPixels);
this.costs = new Float32Array(numPixels);
}
public startSearch(startPoint: Types.Point2): void {
const startPointIndex = this._getPointIndex(startPoint[1], startPoint[0]);
this.startPoint = null;
this.visited.fill(false);
this.parents.fill(MAX_UINT32);
this.costs.fill(Infinity);
this.priorityQueueNew = new BucketQueue<number>({
numBits: this.searchGranularityBits,
getPriority: this._getPointCost,
});
this.startPoint = startPoint;
this.costs[startPointIndex] = 0;
this.priorityQueueNew.push(startPointIndex);
}
/**
* Finds a nearby point with a minimum cost nearby
*
* @param testPoint - to look nearby
* @param delta - how long a distance to look
* @returns A point having the minimum weighted distance from the testPoint
*/
public findMinNearby(testPoint: Types.Point2, delta = 2) {
const [x, y] = testPoint;
const { costs } = this;
const xRange = [
Math.max(0, x - delta),
Math.min(x + delta + 1, this.width),
];
const yRange = [
Math.max(0, y - delta),
Math.min(y + delta + 1, this.height),
];
let minValue = costs[this._getPointIndex(y, x)] * 0.8;
let minPoint = testPoint;
for (let xTest = xRange[0]; xTest < xRange[1]; xTest++) {
for (let yTest = yRange[0]; yTest < yRange[1]; yTest++) {
// Cost values are 0...1, with 1 being a poor choice for the
// livewire fitting - thus, we want to minimize our value, so the
// distance cost should be low for the center point.
const distanceCost =
1 -
(Math.abs(xTest - testPoint[0]) + Math.abs(yTest - testPoint[1])) /
delta /
2;
const weightCost = costs[this._getPointIndex(yTest, xTest)];
const weight = weightCost * 0.8 + distanceCost * 0.2;
if (weight < minValue) {
minPoint = [xTest, yTest];
minValue = weight;
}
}
}
return minPoint;
}
/**
* Runs Dijsktra until it finds a path from the start point to the target
* point. Once it reaches the target point all the state is preserved in order
* to save processing time the next time the method is called for a new target
* point. The search is restarted whenever `startSearch` is called.
* @param targetPoint - Target point
* @returns An array with all points for the shortest path found that goes
* from startPoint to targetPoint.
*/
public findPathToPoint(targetPoint: Types.Point2): Types.Point2[] {
if (!this.startPoint) {
throw new Error('There is no search in progress');
}
const {
startPoint,
_getPointIndex: index,
_getPointCoordinate: coord,
} = this;
const startPointIndex = index(startPoint[1], startPoint[0]);
const targetPointIndex = index(targetPoint[1], targetPoint[0]);
const {
visited: visited,
parents: parents,
costs: cost,
priorityQueueNew: priorityQueue,
} = this;
if (targetPointIndex === startPointIndex) {
return [];
}
// Stop searching until there are no more items in the queue or it has
// reached the target point. In case it reaches the target all the remaining
// items will stay in the queue then once the user moves the mouse to a new
// location the search can continue from where it left off.
while (
!priorityQueue.isEmpty() &&
parents[targetPointIndex] === MAX_UINT32
) {
const pointIndex = priorityQueue.pop();
if (visited[pointIndex]) {
continue;
}
const point = coord(pointIndex);
const neighborsPoints = this._getNeighborPoints(point);
visited[pointIndex] = true;
// Update the cost of all neighbors that have higher costs
for (let i = 0, len = neighborsPoints.length; i < len; i++) {
const neighborPoint = neighborsPoints[i];
const neighborPointIndex = index(neighborPoint[1], neighborPoint[0]);
const dist = this._getWeightedDistance(point, neighborPoint);
const neighborCost = cost[pointIndex] + dist;
if (neighborCost < cost[neighborPointIndex]) {
if (cost[neighborPointIndex] !== Infinity) {
// The item needs to be removed from the priority queue and
// re-added in order to be moved to the right bucket.
priorityQueue.remove(neighborPointIndex);
}
cost[neighborPointIndex] = neighborCost;
parents[neighborPointIndex] = pointIndex;
priorityQueue.push(neighborPointIndex);
}
}
}
const pathPoints = [];
let pathPointIndex = targetPointIndex;
while (pathPointIndex !== MAX_UINT32) {
pathPoints.push(coord(pathPointIndex));
pathPointIndex = parents[pathPointIndex];
}
return pathPoints.reverse();
}
/**
* Convert a point coordinate (x,y) into a point index
* @param index - Point index
* @returns Point coordinate (x,y)
*/
private _getPointIndex = (row: number, col: number) => {
const { width } = this;
return row * width + col;
};
/**
* Convert a point index into a point coordinate (x,y)
* @param index - Point index
* @returns Point coordinate (x,y)
*/
private _getPointCoordinate = (index: number): Types.Point2 => {
const x = index % this.width;
const y = Math.floor(index / this.width);
return [x, y];
};
/**
* Calculate the delta X between a given point and its neighbor at the right
* @param x - Point x-coordinate
* @param y - Point y-coordinate
* @returns Delta Y between the given point and its neighbor at the right
*/
private _getDeltaX(x: number, y: number) {
const { grayscalePixelData: data, width } = this;
let index = this._getPointIndex(y, x);
// If it is at the end, back up one
if (x + 1 === width) {
index--;
}
return data[index + 1] - data[index];
}
/**
* Calculate the delta Y between a given point and its neighbor at the bottom
* @param x - Point x-coordinate
* @param y - Point y-coordinate
* @returns Delta Y between the given point and its neighbor at the bottom
*/
private _getDeltaY(x: number, y: number) {
const { grayscalePixelData: data, width, height } = this;
let index = this._getPointIndex(y, x);
// If it is at the end, back up one
if (y + 1 === height) {
index -= width;
}
return data[index] - data[index + width];
}
private _getGradientMagnitude(x: number, y: number): number {
const dx = this._getDeltaX(x, y);
const dy = this._getDeltaY(x, y);
return Math.sqrt(dx * dx + dy * dy);
}
/**
* Calculate the Laplacian of Gaussian (LoG) value for a given pixel
*
* Kernel Indexes Laplacian of Gaussian Kernel
* __ __ 02 __ __ 0 0 1 0 0
* __ 11 12 13 __ 0 1 2 1 0
* 20 21 22 23 24 1 2 -16 2 1
* __ 31 32 33 __ 0 1 2 1 0
* __ __ 42 __ __ 0 0 1 0 0
*/
private _getLaplace(x: number, y: number): number {
const { grayscalePixelData: data, _getPointIndex: index } = this;
// Points related to the kernel indexes
const p02 = data[index(y - 2, x)];
const p11 = data[index(y - 1, x - 1)];
const p12 = data[index(y - 1, x)];
const p13 = data[index(y - 1, x + 1)];
const p20 = data[index(y, x - 2)];
const p21 = data[index(y, x - 1)];
const p22 = data[index(y, x)];
const p23 = data[index(y, x + 1)];
const p24 = data[index(y, x + 2)];
const p31 = data[index(y + 1, x - 1)];
const p32 = data[index(y + 1, x)];
const p33 = data[index(y + 1, x + 1)];
const p42 = data[index(y + 2, x)];
// Laplacian of Gaussian
let lap = p02;
lap += p11 + 2 * p12 + p13;
lap += p20 + 2 * p21 - 16 * p22 + 2 * p23 + p24;
lap += p31 + 2 * p32 + p33;
lap += p42;
return lap;
}
/**
* Returns a 2D array of gradient magnitude values for grayscale. The values
* are scaled between 0 and 1, and then flipped, so that it works as a cost
* function.
* @returns A gradient object
*/
private _computeGradient(): Float32Array {
const { width, height } = this;
const gradient = new Float32Array(width * height);
let pixelIndex = 0;
let max = 0;
let x = 0;
let y = 0;
for (y = 0; y < height - 1; y++) {
for (x = 0; x < width - 1; x++) {
gradient[pixelIndex] = this._getGradientMagnitude(x, y);
max = Math.max(gradient[pixelIndex], max);
pixelIndex++;
}
// Make the last column the same as the previous one because there is
// no way to calculate `dx` since x+1 gets out of bounds
gradient[pixelIndex] = gradient[pixelIndex - 1];
pixelIndex++;
}
// Make the last row the same as the previous one because there is
// no way to calculate `dy` since y+1 gets out of bounds
for (let len = gradient.length; pixelIndex < len; pixelIndex++) {
gradient[pixelIndex] = gradient[pixelIndex - width];
}
// Flip and scale
for (let i = 0, len = gradient.length; i < len; i++) {
gradient[i] = 1 - gradient[i] / max;
}
return gradient;
}
/**
* Returns a 2D array of Laplacian of Gaussian values
*
* @param grayscale - The input grayscale
* @returns A laplace object
*/
private _computeLaplace(): Float32Array {
const { width, height, _getPointIndex: index } = this;
const laplace = new Float32Array(width * height);
// Make the first two rows low cost
laplace.fill(1, 0, index(2, 0));
for (let y = 2; y < height - 2; y++) {
// Make the first two columns low cost
laplace[index(y, 0)] = 1;
laplace[index(y, 1)] = 1;
for (let x = 2; x < width - 2; x++) {
// Threshold needed to get rid of clutter.
laplace[index(y, x)] = this._getLaplace(x, y) > 0.33 ? 0 : 1;
}
// Make the last two columns low cost
laplace[index(y, width - 2)] = 1;
laplace[index(y, width - 1)] = 1;
}
// Make the last two rows low cost
laplace.fill(1, index(height - 2, 0));
return laplace;
}
/**
* Returns 2D array of x-gradient values for grayscale
*
* @param grayscale - Grayscale pixel data
* @returns 2D x-gradient array
*/
private _computeGradientX(): Float32Array {
const { width, height } = this;
const gradX = new Float32Array(width * height);
let pixelIndex = 0;
for (let y = 0; y < height; y++) {
for (let x = 0; x < width; x++) {
gradX[pixelIndex++] = this._getDeltaX(x, y);
}
}
return gradX;
}
/**
* Compute the Y gradient.
*
* @param grayscale - Grayscale pixel data
* @returns 2D array of y-gradient values for grayscale
*/
private _computeGradientY(): Float32Array {
const { width, height } = this;
const gradY = new Float32Array(width * height);
let pixelIndex = 0;
for (let y = 0; y < height; y++) {
for (let x = 0; x < width; x++) {
gradY[pixelIndex++] = this._getDeltaY(x, y);
}
}
return gradY;
}
/**
* Compute the gradient unit vector.
* @param px - Point x-coordinate
* @param py - Point y-coordinate
* @returns Gradient vector at (px, py), scaled to a magnitude of 1
*/
private _getGradientUnitVector(px: number, py: number) {
const { gradXNew, gradYNew, _getPointIndex: index } = this;
const pointGradX = gradXNew[index(py, px)];
const pointGradY = gradYNew[index(py, px)];
let gradVecLen = Math.sqrt(
pointGradX * pointGradX + pointGradY * pointGradY
);
// To avoid possible divide-by-0 errors
gradVecLen = Math.max(gradVecLen, 1e-100);
return [pointGradX / gradVecLen, pointGradY / gradVecLen];
}
/**
* Compute the gradient direction, in radians, between two points
*
* @param px - Point `p` x-coordinate of point p.
* @param py - Point `p` y-coordinate of point p.
* @param qx - Point `q` x-coordinate of point q.
* @param qy - Point `q` y-coordinate of point q.
* @returns Gradient direction
*/
private _getGradientDirection(
px: number,
py: number,
qx: number,
qy: number
): number {
const dgpUnitVec = this._getGradientUnitVector(px, py);
const gdqUnitVec = this._getGradientUnitVector(qx, qy);
let dp = dgpUnitVec[1] * (qx - px) - dgpUnitVec[0] * (qy - py);
let dq = gdqUnitVec[1] * (qx - px) - gdqUnitVec[0] * (qy - py);
// Make sure dp is positive, to keep things consistent
if (dp < 0) {
dp = -dp;
dq = -dq;
}
if (px !== qx && py !== qy) {
// It's going diagonally between pixels
dp *= Math.SQRT1_2;
dq *= Math.SQRT1_2;
}
dq = Math.min(Math.max(dq, -1), 1);
const direction =
TWO_THIRD_PI * (Math.acos(Math.min(dp, 1)) + Math.acos(dq));
if (isNaN(direction) || !isFinite(direction)) {
console.warn('Found non-direction:', px, py, qx, qy, dp, dq, direction);
return 1;
}
return direction;
}
/** Gets the cost to go from A to B */
public getCost(pointA, pointB): number {
return this._getWeightedDistance(pointA, pointB);
}
/**
* Return a weighted distance between two points
*/
private _getWeightedDistance(pointA: Types.Point2, pointB: Types.Point2) {
const { _getPointIndex: index, width, height } = this;
const [aX, aY] = pointA;
const [bX, bY] = pointB;
// Assign a cost of 1 to any points outside the image, prevents using invalid
// points
if (bX < 0 || bX >= width || bY < 0 || bY >= height) {
return 1;
}
// Use a cost of 0 if the point was outside and is now going inside
if (aX < 0 || aY < 0 || aX >= width || aY >= height) {
return 0;
}
const bIndex = index(bY, bX);
// Weighted distance function
let gradient = this.gradMagnitude[bIndex];
if (aX === bX || aY === bY) {
// The distance is Euclidean-ish; non-diagonal edges should be shorter
gradient *= Math.SQRT1_2;
}
const laplace = this.laplace[bIndex];
const direction = this._getGradientDirection(aX, aY, bX, bY);
return 0.43 * gradient + 0.43 * laplace + 0.11 * direction;
}
/**
* Get up to 8 neighbors points
* @param point - Reference point
* @returns Up to eight neighbor points
*/
private _getNeighborPoints(point: Types.Point2): Types.Point2[] {
const { width, height } = this;
const list: Types.Point2[] = [];
const sx = Math.max(point[0] - 1, 0);
const sy = Math.max(point[1] - 1, 0);
const ex = Math.min(point[0] + 1, width - 1);
const ey = Math.min(point[1] + 1, height - 1);
for (let y = sy; y <= ey; y++) {
for (let x = sx; x <= ex; x++) {
if (x !== point[0] || y !== point[1]) {
list.push([x, y]);
}
}
}
return list;
}
private _getPointCost = (pointIndex: number): number => {
return Math.round(this.searchGranularity * this.costs[pointIndex]);
};
/**
* Create a livewire scissor instance from RAW pixel data
* @param pixelData - Raw pixel data
* @param width - Width of the image
* @param height - Height of the image
* @param voiRange - VOI Range
* @returns A LivewireScissors instance
*/
public static createInstanceFromRawPixelData(
pixelData: Float32Array,
width: number,
height: number,
voiRange: Types.VOIRange
) {
const numPixels = pixelData.length;
const grayscalePixelData = new Float32Array(numPixels);
const { lower: minPixelValue, upper: maxPixelValue } = voiRange;
const pixelRange = maxPixelValue - minPixelValue;
for (let i = 0, len = pixelData.length; i < len; i++) {
// Grayscale values must be between 0 and 1
grayscalePixelData[i] = Math.max(
0,
Math.min(1, (pixelData[i] - minPixelValue) / pixelRange)
);
}
return new LivewireScissors(grayscalePixelData, width, height);
}
}
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