【图像处理】MATLAB：图像压缩

图像压缩背景知识

编码冗余

function h = entropy(x, n)
% 熵

error(nargchk(1, 2, nargin));         % Check input arguments
if nargin < 2
n = 256;                           % Default for n.
end

x = double(x);                        % Make input double
xh = hist(x(:), n);                   % Compute N-bin histogram
xh = xh / sum(xh(:));                 % Compute probabilities

% Make mask to eliminate 0's since log2(0) = -inf.
i = find(xh);

h = -sum(xh(i) .* log2(xh(i)));       % Compute entropy

function CODE = huffman(p)
% 虽然递归比较绕，但仔细分析还是能懂

% Check the input arguments for reasonableness.
error(nargchk(1, 1, nargin));
if (ndims(p) ~= 2) | (min(size(p)) > 1) | ~isreal(p) | ~isnumeric(p)
error('P must be a real numeric vector.');
end

% Global variable surviving all recursions of function 'makecode'
global CODE
CODE = cell(length(p), 1);  % Init the global cell array

if length(p) > 1            % When more than one symbol ...
p = p / sum(p);          % Normalize the input probabilities
s = reduce(p);           % Do Huffman source symbol reductions
makecode(s, []);         % Recursively generate the code
else
CODE = {'1'};            % Else, trivial one symbol case!
end;

%-------------------------------------------------------------------%
function s = reduce(p);
% Create a Huffman source reduction tree in a MATLAB cell structure
% by performing source symbol reductions until there are only two
% reduced symbols remaining

s = cell(length(p), 1);

% Generate a starting tree with symbol nodes 1, 2, 3, ... to
% reference the symbol probabilities.
for i = 1:length(p)
s{i} = i;
end

while numel(s) > 2
[p, i] = sort(p);    % Sort the symbol probabilities
p(2) = p(1) + p(2);  % Merge the 2 lowest probabilities
p(1) = [];           % and prune the lowest one

s = s(i);            % Reorder tree for new probabilities
s{2} = {s{1}, s{2}}; % and merge & prune its nodes
s(1) = [];           % to match the probabilities
end

%-------------------------------------------------------------------%
function makecode(sc, codeword)
% Scan the nodes of a Huffman source reduction tree recursively to
% generate the indicated variable length code words.

% Global variable surviving all recursive calls
global CODE

if isa(sc, 'cell')                   % For cell array nodes,
makecode(sc{1}, [codeword 0]);    % add a 0 if the 1st element
makecode(sc{2}, [codeword 1]);    % or a 1 if the 2nd
else                                 % For leaf (numeric) nodes,
CODE{sc} = char('0' + codeword);  % create a char code string                     % 字符串'0' + codeword即为'codeword'
end

像素间冗余

心理视觉冗余

function y = quantize(x, b, type)

error(nargchk(2, 3, nargin));         % Check input arguments
if ndims(x) ~= 2 | ~isreal(x) | ...
~isnumeric(x) | ~isa(x, 'uint8')
error('The input must be a UINT8 numeric matrix.');
end

% Create bit masks for the quantization
lo = uint8(2 ^ (8 - b) - 1);
hi = uint8(2 ^ 8 - double(lo) - 1);

% Perform standard quantization unless IGS is specified
if nargin < 3 | ~strcmpi(type, 'igs')
y = bitand(x, hi);

else
[m, n] = size(x);
c2ed

s = zeros(m, 1);
hitest = double(bitand(x, hi) ~= hi);
x = double(x);
for j = 1:n
s = x(:, j) + hitest(:, j) .*double(bitand(uint8(s), lo));
y(:, j) = bitand(uint8(s), hi);
end
end

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