DCTN - N-D discrete cosine transform.

Y = DCTN(X) returns the discrete cosine transform (DCT) of X. The array Y is the same size as X and contains the discrete cosine transform coefficients. This transform can be inverted using IDCTN.

DCTN(X,DIM) applies the DCT operation across the dimension DIM.

Contents

Example #1: Remove high frequencies in an image using DCT

RGB = imread('autumn.tif');
I = rgb2gray(RGB);

DCT transform:

J = dctn(I);
imshow(log(abs(J)),[]), title('DCT coefficients (log scale)')
colormap(gca,jet(64)), colorbar

The commands below set values less than magnitude 10 in the DCT matrix to zero, then reconstruct the image using the inverse DCT.

J(abs(J)<10) = 0;
spy(J), axis off, title('Non-zero coefficients'), snapnow
disp(['number of zeros: ' int2str(100-round(nnz(J)/numel(J)*100)) '%'])
K = idctn(J);
imshow(I), title('Original image'), snapnow
imshow(K,[0 255]), title('DCT-processed image')

number of zeros: 77%

Example #2: JPEG compression

I = imread('cameraman.tif');
imshow(I), title('Original image')
I = int8(double(I)-128);

Compute the 2-D DCT of each 8-by-8 block of the image:

J = blockproc(I,[8 8],@(x) dctn(x.data));
imshow(J,[]), title('DCT coefficients')
colormap(gca,parula(64)), colorbar

The base quantization matrix is

Q50 = [16 11 10 16 24 40 51 61; 12 12 14 19 26 58 60 55; ...
       14 13 16 24 40 57 69 56; 14 17 22 29 51 87 80 62; ...
       18 22 37 56 68 109 103 77; 24 35 55 64 81 104 113 92; ...
       49 64 78 87 103 121 120 101; 72 92 95 98 112 100 103 99]

Q50 =

    16    11    10    16    24    40    51    61
    12    12    14    19    26    58    60    55
    14    13    16    24    40    57    69    56
    14    17    22    29    51    87    80    62
    18    22    37    56    68   109   103    77
    24    35    55    64    81   104   113    92
    49    64    78    87   103   121   120   101
    72    92    95    98   112   100   103    99

Quantization:

C = blockproc(J,[8 8],@(x) round(x.data./Q50));
imshow(C,[]), title('Compressed image')
disp(['number of zeros: ' int2str(100-round(nnz(C)/numel(C)*100)) '%'])

number of zeros: 85%

Note that the coding and decoding processes are beyond the scope of this example.

Decompression:

J2 = blockproc(C,[8 8],@(x) round(x.data.*Q50));
I2 = uint8(blockproc(J2,[8 8],@(x) idctn(x.data))+128);
imshow(I2), title('Decompressed image')

Reference

Narasimha MJ and Peterson AM, On the computation of the discrete cosine transform, IEEE Trans. Comm. 1978;26:934-936.

See also

dct, dct2, idctn

About the author

Damien Garcia, Eng., Ph.D.
INSERM researcher
Creatis, University of Lyon, France

website: BioméCardio


Published with MATLAB® R2017a