1.軟體版本
MATLAB2021a
2.本算法理論知識
提出了一種”基于小波變換的多尺度自适應雙邊濾波器“算法。
其對應的算法流程如下所示:
下面,我們從理論上限介紹一下這裡所采用的改進後的算法。
第一:多尺度圖像的自适應雙邊濾波
這個部分,是我們這裡所需要研究的創新的算法,這裡重點從理論上介紹一下。
首先通過圖像亮度,将圖像區分為前景圖和背景圖。
這裡,我們主要通過二值話處理,進行圖像的前景和背景的區分,這個部分的理論為:
這裡,門限T的計算,我們主要通過matlab自帶的一個函數獲得,這個函數會根據每個圖像自動計算出門限T。
graythresh
對于的代碼為:
然後分别對前景和背景進行sigma參數的自适應調整。
這裡,sigma的計算公式為:
這裡,我們根據上面的背景前景,做如下的設定。
這裡,我們分别對前景和背景下乘以系數K1和K2,其中根據亮度分布(亮的為背景、暗的為物體)來确定BF的各像素的兩個sigma值,讓亮區域平滑更多(選用大sigma),暗區域平滑偏小(小sigma)。
3.核心代碼
% Pre-process input and select appropriate filter.
function B = bfilter2(A,w,sigma)
% Verify that the input image exists and is valid.
if ~exist('A','var') || isempty(A)
error('Input image A is undefined or invalid.');
end
if ~isfloat(A) || ~sum([1,3] == size(A,3)) || ...
min(A(:)) < 0 || max(A(:)) > 1
error(['Input image A must be a double precision ',...
'matrix of size NxMx1 or NxMx3 on the closed ',...
'interval [0,1].']);
end
% Verify bilateral filter window size.
if ~exist('w','var') || isempty(w) || ...
numel(w) ~= 1 || w < 1
w = 5;
end
w = ceil(w);
% Verify bilateral filter standard deviations.
if ~exist('sigma','var') || isempty(sigma) || ...
numel(sigma) ~= 2 || sigma(1) <= 0 || sigma(2) <= 0
sigma = [3 0.1];
end
% Apply either grayscale or color bilateral filtering.
if size(A,3) == 1
B = bfltGray(A,w,sigma(1),sigma(2));
else
B = bfltColor(A,w,sigma(1),sigma(2));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Implements bilateral filtering for grayscale images.
function B = bfltGray(A,w,sigma_d,sigma_r)
% Pre-compute Gaussian distance weights.
[X,Y] = meshgrid(-w:w,-w:w);
G = exp(-(X.^2+Y.^2)/(2*sigma_d^2));
% Create waitbar.
h = waitbar(0,'Applying bilateral filter...');
set(h,'Name','Bilateral Filter Progress');
% Apply bilateral filter.
dim = size(A);
B = zeros(dim);
for i = 1:dim(1)
for j = 1:dim(2)
% Extract local region.
iMin = max(i-w,1);
iMax = min(i+w,dim(1));
jMin = max(j-w,1);
jMax = min(j+w,dim(2));
I = A(iMin:iMax,jMin:jMax);
% Compute Gaussian intensity weights.
H = exp(-(I-A(i,j)).^2/(2*sigma_r^2));
% Calculate bilateral filter response.
F = H.*G((iMin:iMax)-i+w+1,(jMin:jMax)-j+w+1);
B(i,j) = sum(F(:).*I(:))/sum(F(:));
end
waitbar(i/dim(1));
end
% Close waitbar.
close(h);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Implements bilateral filter for color images.
function B = bfltColor(A,w,sigma_d,sigma_r)
% Convert input sRGB image to CIELab color space.
if exist('applycform','file')
A = applycform(A,makecform('srgb2lab'));
else
A = colorspace('Lab<-RGB',A);
end
% Pre-compute Gaussian domain weights.
[X,Y] = meshgrid(-w:w,-w:w);
G = exp(-(X.^2+Y.^2)/(2*sigma_d^2));
% Rescale range variance (using maximum luminance).
sigma_r = 100*sigma_r;
% Create waitbar.
h = waitbar(0,'Applying bilateral filter...');
set(h,'Name','Bilateral Filter Progress');
% Apply bilateral filter.
dim = size(A);
B = zeros(dim);
for i = 1:dim(1)
for j = 1:dim(2)
% Extract local region.
iMin = max(i-w,1);
iMax = min(i+w,dim(1));
jMin = max(j-w,1);
jMax = min(j+w,dim(2));
I = A(iMin:iMax,jMin:jMax,:);
% Compute Gaussian range weights.
dL = I(:,:,1)-A(i,j,1);
da = I(:,:,2)-A(i,j,2);
db = I(:,:,3)-A(i,j,3);
H = exp(-(dL.^2+da.^2+db.^2)/(2*sigma_r^2));
% Calculate bilateral filter response.
F = H.*G((iMin:iMax)-i+w+1,(jMin:jMax)-j+w+1);
norm_F = sum(F(:));
B(i,j,1) = sum(sum(F.*I(:,:,1)))/norm_F;
B(i,j,2) = sum(sum(F.*I(:,:,2)))/norm_F;
B(i,j,3) = sum(sum(F.*I(:,:,3)))/norm_F;
end
waitbar(i/dim(1));
end
% Convert filtered image back to sRGB color space.
if exist('applycform','file')
B = applycform(B,makecform('lab2srgb'));
else
B = colorspace('RGB<-Lab',B);
end
% Close waitbar.
close(h);
4.操作步驟與仿真結論
5.參考文獻