AIM: Study and Implementation of Discrete Cosine Transform of
given image.
For DCT:
THEORY:
Discrete
Cosine Transform (DCT) has been an important achievement in the field of image
compression. The DCT can be considered as a discrete time version of the
Fourier Cosine series. The discrete cosine transforms (DCT) is a technique for
converting a signal into elementary frequency components. The transformed array
obtained through DCT is also of the size N x N, same as that of the original
image block.
Such fast computational approaches and use of real arithmetic has made DCT popular for image compression applications. Since all natural images exhibits spatial redundancy, not all coefficients in the transformed array have significant values.
Such fast computational approaches and use of real arithmetic has made DCT popular for image compression applications. Since all natural images exhibits spatial redundancy, not all coefficients in the transformed array have significant values.
Applications:
1. Popular JPEG file
format, and most video compression methods are generally based on it.
2. DCT make an image
compression standard in stillimage and multimedia coding standards.
Advantages:
1.
DCT uses image independent transformations.
2.
DCT has high energy compaction property.
3.
Fast algorithms and architectures are available for DCT
4.
DCT uses real computations, unlike the complex computations used in DFT. This
makes DCT hardware simpler, as compared to that of DFT.
Limitations:
Despite excellent energy compaction
capabilities, meansquare reconstruction error performance closely matching that
of KLT and availability of fast computational approaches, DCT offers a few
limitations which restrict its use in very low bit rate applications. The
limitations are listed below:
1. Truncation of higher spectral coefficients
results in blurring of the images, especially wherever the details are high.
2. Coarse quantization of some of the low
spectral coefficients introduces graininess in the smooth portions of the
images.
3. Serious blocking artifacts are
introduced at the block boundaries, since each block is independently encoded,
often with a different encoding strategy and the extent of quantization.
Following equation shows 2D DCT:
Syntax for DCT and IDCT:
For DCT:
2D
discrete cosine transforms.
B =
dct2(A)

Returns the twodimensional discrete cosine
transform of A. The matrix B is the same size as A and contains the discrete
cosine transform coefficients B(k1,k2).
B =
dct2(A,m,n)

pads the matrix A with 0's to size mbyn
before transforming. If m or n is smaller than the corresponding dimension of A, dct2 truncates
A.
B = dct2(A,[m
n])

Same as above.
For IDCT:
IDCT2 2D inverse discrete
cosine transform.
B =
IDCT2(A)

Returns the twodimensional
inverse discrete cosine transform of A.
B = IDCT2
(A,[M N]) or B = IDCT2(A,M,N)

Pads A with zeros (or truncates
A) to create a matrix of size MbyN before transforming.
PROGRAM:
Function of DCT for Color & Grayscale image:
function
out=mydct2(img)
[r c p]=size(img);
if(p==3)
out(:,:,1)=dct2(img(:,:,1));
out(:,:,2)=dct2(img(:,:,2));
out(:,:,3)=dct2(img(:,:,3));
else
out=dct2(img);
end

Function of IDCT for Color & Grayscale image:
function
rec=myidct2(img)
[r c p]=size(img);
if(p==3)
rec(:,:,1)=idct2(img(:,:,1));
rec(:,:,2)=idct2(img(:,:,2));
rec(:,:,3)=idct2(img(:,:,3));
else
rec=idct2(img);
end

Test Application:
[file path]=uigetfile('*.*');
img=imread(file);
out=mydct2(img);
rec=myidct2(out);
subplot(1,3,1);imshow(img);title('Original Image')
subplot(1,3,2);imshow(uint8(out));title('DCT of I/P Image')
subplot(1,3,3);imshow(uint8(rec));title('Rec image')

Outputs:
For Color Image:
For Grayscale Image:
Dear Sir,
ReplyDeleteDo you have any code for the quantization and the zipzap reorder.
hi, do you hae any code for quantization please ?
ReplyDelete