Resizing Color Images in the Compressed Domain
Jayanta Mukherjee and Sanjit K. Mitra

6.1 Introduction ...............................................................................................................
6.2 Image Resizing Techniques .............................................................................................
      6.2.1 Using Linear, Distributive, and Unitary Transform Properties ..............................................
      6.2.2 Using Convolution–Multiplication Properties ...................................................................
      6.2.3 Using Subband DCT Approximation .............................................................................
               6.2.3.1 Image Doubling: A Case Study .........................................................................
6.3 Image-Halving and Image-Doubling Algorithms Revisited ..........................................................
      6.3.1 Image Halving ....................................................................................................
      6.3.2 Image Doubling ...................................................................................................
6.4 Resizing with Arbitrary Factors ........................................................................................
      6.4.1 Resizing with Integral Factors ..................................................................................
      6.4.2 Computational Cost ..............................................................................................
      6.4.3 Resizing with Rational Factors .................................................................................
6.5 Color Image Resizing ...................................................................................................
6.6 Concluding Remarks ....................................................................................................
Acknowledgements ..........................................................................................................
Appendix: Mathematical Preliminaries ....................................................................................
      6.6.1 DCT: Definitions and Notations ................................................................................
               6.6.1.1 2-D DCT ..................................................................................................
               6.6.1.2 Matrix Representation .................................................................................
      6.6.2 Downsampling and Upsampling Properties of the DCTs .....................................................
      6.6.3 Subband Relationship of the Type-II DCT .....................................................................
               6.6.3.1 Approximate DCT Computation .......................................................................
               6.6.3.2 Approximate DCT in 2-D ...............................................................................
      6.6.4 Recomposition and Decomposition of the DCT Blocks .......................................................
      6.6.5 Symmetric Convolution and Convolution–Multiplication Properties in DCT Domain .......................
               6.6.5.1 Extension to 2-D ........................................................................................
References ....................................................................................................................