1. 概述
以前一直觉得热力图非常高大上，现在终于有机会研究并总结这个问题了。其实从图像处理的角度上来说，热力图生成算法并没有什么特别的，要得到非常漂亮的效果，数据以及配色方案的也很重要。这里就用OpenCV简单实现一下，用什么工具不重要，重要的是其中的原理。
2. 详论
2.1. 数据准备
我们没有数据，但是可以通过随机数算法，生成一个热力点的集合：
struct HPoint {
int x;
int y;
int value;
};
int width = 512; //热力图宽
int height = 512; //热力图高
int reach = 25; //影响范围
int valueRange = 100;
vector<HPoint> heatPoints; //热力点
vector<HRect> heatRects; //热力范围
void GetHeatPoint() {
int num = 100;
heatPoints.resize(num);
heatRects.resize(num);
for (int i = 0; i < num; i++) {
heatPoints[i].x = rand() % width;
heatPoints[i].y = rand() % height;
heatPoints[i].value = rand() % valueRange;
heatRects[i].left = (std::max)(heatPoints[i].x - reach, 0);
heatRects[i].top = (std::max)(heatPoints[i].y - reach, 0);
heatRects[i].right = (std::min)(heatPoints[i].x + reach, width - 1);
heatRects[i].bottom = (std::min)(heatPoints[i].y + reach, height - 1);
}
}
这段代码的意思是，我们根据给定的热力图宽高的范围，生成热力图范围内一定权值范围的热力点；并且，根据热力点影响范围求出其外包矩形。这里的随机数并没有给时间种子，所以每次运行的结果都是固定的。
2.2. 准备绘制
我们绘制的目的是一个包含透明度的彩色图片，所以需要创建4波段的图片。通过直接操作图片的内存buffer，首先我们将背景设置成黑色；然后遍历热力点，将热力点的范围涂成白色：
Mat img(height, width, CV_8UC4);
int nBand = 4;
uchar *data = img.data;
size_t dataLength = (size_t)width * height * nBand;
memset(data, 0, dataLength);
for (size_t i = 0; i < heatPoints.size(); i++) {
//遍历热力点范围
for (int hi = heatRects[i].top; hi <= heatRects[i].bottom; hi++) {
for (int wi = heatRects[i].left; wi <= heatRects[i].right; wi++) {
size_t m = (size_t)width * nBand * hi + wi * nBand;
data[m + 0] = data[m + 1] = data[m + 2] = data[m + 3] = 255;
}
}
}
imshow("热力图", img);
waitKey();
2.3. 绘制热力范围
上面绘制的是热力点的外接矩形范围，现在我们绘制热力图真正影响范围。原理其实很简单，就是判断点是否在圆内：
for (size_t i = 0; i < heatPoints.size(); i++) {
//遍历热力点范围
for (int hi = heatRects[i].top; hi <= heatRects[i].bottom; hi++) {
for (int wi = heatRects[i].left; wi <= heatRects[i].right; wi++) {
//判断是否在热力圈范围
float length =
sqrt((float)(wi - heatPoints[i].x) * (wi - heatPoints[i].x) +
(hi - heatPoints[i].y) * (hi - heatPoints[i].y));
if (length <= reach) {
size_t m = (size_t)width * nBand * hi + wi * nBand;
data[m + 0] = data[m + 1] = data[m + 2] = data[m + 3] = 255;
}
}
}
}
2.4. 绘制热力图
接下来就让热力范围根据与热力点的距离渐变：距离越近，就越白，距离越远，就越黑：
for (size_t i = 0; i < heatPoints.size(); i++) {
//遍历热力点范围
for (int hi = heatRects[i].top; hi <= heatRects[i].bottom; hi++) {
for (int wi = heatRects[i].left; wi <= heatRects[i].right; wi++) {
//判断是否在热力圈范围
float length =
sqrt((float)(wi - heatPoints[i].x) * (wi - heatPoints[i].x) +
(hi - heatPoints[i].y) * (hi - heatPoints[i].y));
if (length <= reach) {
float alpha = ((reach - length) / reach);
size_t m = (size_t)width * nBand * hi + wi * nBand;
data[m + 0] = data[m + 1] = data[m + 2] = data[m + 3] = uchar(255 * alpha);
}
}
}
}
立体感到是不错，但是问题在于我们需要将热力点的影响叠加起来，也就是每次遍历热力点之后，像素值也要叠加起来：
for (size_t i = 0; i < heatPoints.size(); i++) {
//遍历热力点范围
for (int hi = heatRects[i].top; hi <= heatRects[i].bottom; hi++) {
for (int wi = heatRects[i].left; wi <= heatRects[i].right; wi++) {
//判断是否在热力圈范围
float length =
sqrt((float)(wi - heatPoints[i].x) * (wi - heatPoints[i].x) +
(hi - heatPoints[i].y) * (hi - heatPoints[i].y));
if (length <= reach) {
float alpha = ((reach - length) / reach);
size_t m = (size_t)width * nBand * hi + wi * nBand;
float newAlpha = data[m + 3] / 255.0f + alpha;
newAlpha = std::min(std::max(newAlpha * 255, 0.0f), 255.0f);
data[m + 0] = data[m + 1] = data[m + 2] = data[m + 3] =
uchar(newAlpha);
}
}
}
}
看起来略具意思了，但是有个问题是没有体现每个点的权值的影响，因此我们加上权值的影响，让热力的效果更真实一点：
for (size_t i = 0; i < heatPoints.size(); i++) {
//权值因子
float ratio = (float)heatPoints[i].value / valueRange;
//遍历热力点范围
for (int hi = heatRects[i].top; hi <= heatRects[i].bottom; hi++) {
for (int wi = heatRects[i].left; wi <= heatRects[i].right; wi++) {
//判断是否在热力圈范围
float length =
sqrt((float)(wi - heatPoints[i].x) * (wi - heatPoints[i].x) +
(hi - heatPoints[i].y) * (hi - heatPoints[i].y));
if (length <= reach) {
float alpha = ((reach - length) / reach) * ratio;
size_t m = (size_t)width * nBand * hi + wi * nBand;
float newAlpha = data[m + 3] / 255.0f + alpha;
newAlpha = std::min(std::max(newAlpha * 255, 0.0f), 255.0f);
data[m + 0] = data[m + 1] = data[m + 2] = data[m + 3] =
uchar(newAlpha);
}
}
}
}
2.5. 配色方案
最后就是给这个黑白热力图上色了。配色是非常重要的，需要一点美术功底才行，我们直接采用参考2中的颜色值进行配色。首先创建一个颜色映射表，将之前的黑白色映射到一个BGR渐变色集合：
array<array<uchar, 3>, 256> bGRTable; //颜色映射表
//生成渐变色
void Gradient(array<uchar, 3> &start, array<uchar, 3> &end,
vector<array<uchar, 3>> &RGBList) {
array<float, 3> dBgr;
for (int i = 0; i < 3; i++) {
dBgr[i] = (float)(end[i] - start[i]) / (RGBList.size() - 1);
}
for (size_t i = 0; i < RGBList.size(); i++) {
for (int j = 0; j < 3; j++) {
RGBList[i][j] = (uchar)(start[j] + dBgr[j] * i);
}
}
}
void InitAlpha2BGRTable() {
array<double, 7> boundaryValue = {0.2, 0.3, 0.4, 0.6, 0.8, 0.9, 1.0};
array<array<uchar, 3>, 7> boundaryBGR;
boundaryBGR[0] = {255, 0, 0};
boundaryBGR[1] = {231, 111, 43};
boundaryBGR[2] = {241, 192, 2};
boundaryBGR[3] = {148, 222, 44};
boundaryBGR[4] = {83, 237, 254};
boundaryBGR[5] = {50, 118, 253};
boundaryBGR[6] = {28, 64, 255};
double lastValue = 0;
array<uchar, 3> lastRGB = {0, 0, 0};
vector<array<uchar, 3>> RGBList;
int sumNum = 0;
for (size_t i = 0; i < boundaryValue.size(); i++) {
int num = 0;
if (i == boundaryValue.size() - 1) {
num = 256 - sumNum;
} else {
num = (int)((boundaryValue[i] - lastValue) * 256 + 0.5);
}
RGBList.resize(num);
Gradient(lastRGB, boundaryBGR[i], RGBList);
for (int i = 0; i < num; i++) {
bGRTable[i + sumNum] = RGBList[i];
}
sumNum = sumNum + num;
lastValue = boundaryValue[i];
lastRGB = boundaryBGR[i];
}
}
通过这个颜色映射表，在填充像素的时候，将计算的Alpha映射成一个BGR值，填充到前三个波段中：
for (size_t i = 0; i < heatPoints.size(); i++) {
//权值因子
float ratio = (float)heatPoints[i].value / valueRange;
//遍历热力点范围
for (int hi = heatRects[i].top; hi <= heatRects[i].bottom; hi++) {
for (int wi = heatRects[i].left; wi <= heatRects[i].right; wi++) {
//判断是否在热力圈范围
float length =
sqrt((float)(wi - heatPoints[i].x) * (wi - heatPoints[i].x) +
(hi - heatPoints[i].y) * (hi - heatPoints[i].y));
if (length <= reach) {
float alpha = ((reach - length) / reach) * ratio;
//计算Alpha
size_t m = (size_t)width * nBand * hi + wi * nBand;
float newAlpha = data[m + 3] / 255.0f + alpha;
newAlpha = std::min(std::max(newAlpha * 255, 0.0f), 255.0f);
data[m + 3] = (uchar)(newAlpha);
//颜色映射
for (int bi = 0; bi < 3; bi++) {
data[m + bi] = bGRTable[data[m + 3]][bi];
}
}
}
}
}
最终的成果如下：
3. 问题
- OpenCV显示的背景是黑色的，这是因为其默认是按照RGB三波段来显示的，其实最后的结果是个包含透明通道的图像，可以将其叠加到任何图层上：
- 热力点可以有权值，也可以没有。没有权值可以认为所有点的权值是一样的，可以适当调整热力影响的范围让不同的热力点连接，否则就是一个个独立的圈。
- 如果出现红色的区域（热力值高）过多，那么原因可能是热力点太密了。同一个区域内收到的热力影响太多，计算的alpha超过1，映射到图像像素值导致被截断，无法区分热力值高的区域。那么一个合理的改进方案就是将计算的alpha缓存住，在计算所有的alpha的最大最小，将alpha再度映射到0到1之间，进而映射到像素值的0~255之间——就不会高位截断的问题了。如果有机会，再实现一下这个问题的改进。