MCNN提出了适用于高密度人群的自适应高斯核：

笔者所理解的自适应高斯核函数：

%function:通过高斯核产生相应的密度矩阵

%parameter： im：输入图像，灰度图； points：标注的点[X Y]，n*2的矩阵

function im_density = get_density_map_autogaussian(im,points)

im_density = zeros(size(im));

[h,w] = size(im_density);

if(isempty(points))

return;

end

%points为1行

if(length(points(:,1))==1)

x1 = max(1,min(w,round(points(1,1)))); %round：四舍五入，x1变成points(1,1)处的整数

y1 = max(1,min(h,round(points(1,2))));

im_density(y1,x1) = 255;

return;

end

for j = 1:length(points)

max_kernel = 65; %最大高斯核尺寸

normal_kernel = 35; %默认高斯核尺寸

beta = 0.3; %MCNN中给定的参数

k = 6; %近邻数

maxpixel = 80; %近邻的最大距离，像素

% f_sz = normal_kernel;

% sigma = beta * f_sz;

x = min(w,max(1,abs(double(floor(points(j,1))))));

y = min(h,max(1,abs(double(floor(points(j,2))))));

if(x > w || y > h)

continue;

end

%--------%auto adaptive 自适应高斯核--------

atemp = [];

for i = 1:length(points)

if i == j

continue;

end

xk = min(w,max(1,abs(double(floor(points(i,1))))));

yk = min(w,max(1,abs(double(floor(points(i,2))))));

if(xk > w || yk > h)

continue;

end

dis = sqrt( ((xk-x)^2 + (yk-y)^2) );

atemp = [atemp dis];

end

btemp = sort(atemp);

sum = 0;

count = 0;

if k >= length(points)

k = length(points) - 1;

end

for m = 1:k

if btemp(m) > maxpixel

break;

end

sum = sum + btemp(m);

count = count + 1;

end

if count > 0

temp = sum/count;

else

temp = normal_kernel;

end

f_sz = double(floor(temp));

if mod(f_sz, 2) == 0

f_sz = double(f_sz + 1);

end

if f_sz > (max_kernel + 1)

f_sz = max_kernel;

end

sigma = beta * f_sz;

% fprintf("x:%d,y:%d,f_sz:%d,sigma：%d\n",x,y,f_sz, sigma);

%--------auto adaptive 自适应高斯核定义结束--------

H = fspecial('Gaussian',[f_sz, f_sz],sigma);

%高斯核边界限定，x方向：→，y方向：↓

x1 = x - double(floor(f_sz/2)); y1 = y - double(floor(f_sz/2)); %x1左边界，y1上边界

x2 = x + double(floor(f_sz/2)); y2 = y + double(floor(f_sz/2)); %x2右边界，y2下边界

dfx1 = 0; dfy1 = 0; dfx2 = 0; dfy2 = 0;

change_H = false;

if(x1 < 1)

dfx1 = abs(x1)+1;

x1 = 1;

change_H = true;

end

if(y1 < 1)

dfy1 = abs(y1)+1;

y1 = 1;

change_H = true;

end

if(x2 > w)

dfx2 = x2 - w;

x2 = w;

change_H = true;

end

if(y2 > h)

dfy2 = y2 - h;

y2 = h;

change_H = true;

end

x1h = 1+dfx1; y1h = 1+dfy1; x2h = f_sz - dfx2; y2h = f_sz - dfy2;

if (change_H == true)

H = fspecial('Gaussian',[double(y2h-y1h+1), double(x2h-x1h+1)],sigma);

end

im_density(y1:y2,x1:x2) = im_density(y1:y2,x1:x2) + H;

end

end

转换为密度图：

i = 45;

dataset = 'A';

path = ['../data/original/shanghaitech/part_' dataset '_final/train_data/images/'];

gt_path = ['../data/original/shanghaitech/part_' dataset '_final/train_data/ground_truth/'];

load(strcat(gt_path, 'GT_IMG_',num2str(i),'.mat')) ;

input_img_name = strcat(path,'IMG_',num2str(i),'.jpg');

im = imread(input_img_name);

[h, w, c] = size(im);

if (c == 3)

im = rgb2gray(im); %转化成[h w 1]的矩阵灰度图

end

figure(1)

imshow(im)

hold on

annPoints = image_info{1}.location;

im_density = get_density_map_autogaussian(im,annPoints);

%sum(sum(im_density))

%im_density = get_density_map_gaussian(im,annPoints);

figure(2)

cmap = colormap(jet(210));

imagesc(im_density,[0 max(max(im_density))])

%imagesc(im_density,[0 0.038])

colorbar

MCNN论文中的插图

与论文插图接近。