如何計算matlab中圖像的總變差

Question

我正試圖使用​​空間一階導數的l1範數計算matlab中圖像的總變差。代碼是波紋管：

function TV = compute_total_variation1(y) 
% y is the image 
nbdims = 2; 

% check number of channels in an image 
if size(y,1)==1 || size(y,2)==1 
    % we have one dimension 
    nbdims = 1; 
end 

if size(y,1)>1 && size(y,2)>1 && size(y,3)>1 
    % we have three dimensions 
    nbdims = 3; 
end 

if nbdims==1 
    TV = sum(abs(diff(y))); 
    return; 
end 

% the total variation weight is 1 
% weight_tv = ones(size(y)); 

g = gradient(y); 
% compute using the l1 norm of the first order derivatives 
TV = sum(abs(g),nbdims+1); 

% TV = TV .* weight_tv; 
TV = sum(TV(:)); 

我是否正確計算使用l1範數的總變差？

編輯：

function TV = compute_total_variation1(y) 
% y is the image 
nbdims = 2; 

% check number of channels in an image 
if size(y,1)==1 || size(y,2)==1 
    % we have one dimension 
    nbdims = 1; 
end 

if size(y,1)>1 && size(y,2)>1 && size(y,3)>1 
    % we have three dimensions 
    nbdims = 3; 
end 

if nbdims==1 
    TV = sum(abs(diff(y))); 
    return; 
end 

% the total variation weight is 1 
% weight_tv = ones(size(y)); 

[gx gy] = gradient(y); 
% compute using the l1 norm of the first order derivatives 
% horizontal 
TVgx = sum(abs(gx),nbdims+1); 
% vertical 
TVgy = sum(abs(gy),nbdims+1); 
% TV = TV .* weight_tv; 
TV = sum(TVgx(:)) + sum(TVgy(:)); 

Answer 1

你不考慮第二昏暗的衍生品：只有

g = gradient(y) 

返回沿水平方向導數，以獲得微分沿着垂直方向，您也需要

[gx, gy] = gradient(y);