Sequence Mirroring Properties of Orthogonal Transforms Having Even and Odd Symmetric Vectors. K. R. Rao

Transcription

1 equence Mirroring Properties of Orthogonal ransforms Having Even and Odd ymmetric Vectors. R. Rao Dept of Electrical Engineering Univ. of eas at Arlington,, UA

2 Research Purpose mage/video coding/compression utilizes discrete orthogonal transforms. Compress images to save storage space or transmit and then edit in the compressed-domain. ransform-domain image mirroring and rotation scheme in this presentation.

3 Previous Works on ransform Domain mage/video Processing mith and Rowe: Video dissolve and caption insert. Linearity of the DC. Chang and Messerschmitt: Reconstruct DC block using neighboring 4 DC blocks. DC is distributive to matri multiplication. Merhav and Bhaskaran: Fast DC-domain bilinear interpolation and motion compensation. hen, ethi and Bhaskaran: logotype insertion. DC-domain convolution which corresponds to multiplication in the spatial domain is more efficient because of the orthogonality of the DC. hen and ethi [7]: DC-domain image flipping scheme

4 ransforms having even and odd symmetric row vectors Let one of these orthogonal matrices be [ ] 4 a c e g b d f h b d f h a c e g even odd even odd As [ 4 ] is orthogonal, [ ][ 4 4 ] [ ]

5 Proposed Algorithm Let be transform coefficients of mirroring a sequence. M M [ ] [ ] 4 J 4 [ ] [ ] 4 4 [ ] 4 [ ] J 4 [ ] diag(,,, ) 4

6 Proposed Algorithm ype orthogonal transforms: DC, D, slant and their integer revisions like ntdc [ ] diag(,,,,,, ) ype 2 orthogonal transforms: Hadamard [ ] diag(,,,,,, ) No such properties: MDC, Haar, Hartley

7 Etension to the 2-D Case mage can be represented as nonoverlapping blocks of size (N N) (for eample N ). Each block: ransform: 2-D transform coeff: 2D-transform of horizontally/vertically mirrored sequence [ ] 7, 2 2 )}, ( { n n n n [ ] 7, )}, ( { n m n m s [ ] [ ] [ ][ ] [ ] [ ][ ] H [ ] [ ][ ] V [ ]

8 wo-dimensional Etension Let represent element-by-element multiplication. he 2D-transforms of the 9, and 27 rotated blocks [ ] [ ][ ] [ ][ ] [ ][ ] [ ] [ ] J o 9 [ ] [ ] [ ] V [ ] [ ][ ][ ] [ ] [ ] W o [ ] [ ][ ][ ] [ ] [ ][ ][ ][ ] J o 27 [ ][ ] [ ] H [ ] W [ ] O O J

9 Video Editing Application elect a group of consecutive 2D-transform blocks of an image Flip horizontally according to the following steps: Apply the ( ) 2D-transform to the nonoverlapping blocks of size ( ) of the image. et the size of a rectangular block to be horizontally flipped. Horizontal and vertical sizes should be multiples of eight according to the transform size. Compute transform -domain image flipping for each transform block by using [ ] [ ][ ] H Rotate horizontally transform blocks within the rectangular block. he most left transform block goes to the most right, and vice versa.

10 Mirroring or Rotation of portion of Lena in spatial domain by manipulating the ntdc coefficients of the original block (a) (c) (d) (b) (e) (a) horizontal mirroring (b) vertical mirroring (c) rotation by 9 (d) rotation by (e) rotation by 27

11 Mirroring or Rotation (a) (c) (d) (b) (e) lant ransform D- Hadamard ransform DC- (a) horizontal mirroring (b) vertical mirroring (c) rotation by 9 (d) rotation by (e) rotation by 27

12 Conclusions We showed sequence mirroring properties of orthogonal transforms having even and odd symmetric vectors As applications, we flip images horizontally and/or vertically in the spatial domain by appropriately changing the signs of the transform coefficients. imilarly rotation of the images are accomplished. his technique does not need any multiplications and only needs to change signs of the D coefficients.

13 References []. R. Rao and P. Yip, he transform and data compression handbook. CRC Press, 2. [2] W.. Cham, Development of integer cosine transforms by the principle of dyadic symmetry, EE Proc., Commu., peech & Vision, vol. 36, pp , Aug. 99. [3] G. J. ullivan, P. opiwala and A. Luthra, he H.264/AVC advanced video coding standard: overview and introduction to the fidelity range etensions, in Proc. PE Conf. on Applications of Digital mage Processing V, pp , Aug. 24. [4]. rinivasan et al., Windows media video 9: overview and applications, ignal Processing: mage Communication, vol. 9, pp. 5-75, Oct. 24. [5] Y.-J. Chen and. Oraintara, Video compression using integer DC, in Proc. EEE CP, pp , ept. 2.

14 References [6] W. Gao et al., AV he Chinese net-generation video coding standard, NAB, Las Vegas, Nevada, April 24. [7] B. hen and.. ethi, nner-block operations on compressed images, in Proc. of the hird ACM nternational Conference on Multimedia, pp , an Francisco CA, 995. [] V. Britanak, P. Yip and. R. Rao, Discrete cosine and sine transforms. Orlando, FL: Academic Press (Elsevier), 27. [9] W.. Pratt, W.-H. Chen and L. R. Welch, lant transform image coding, EEE rans. Commun., vol. 22, pp , Aug [] A.. Jain, Fundamentals of digital image processing, Englewood Cliffs, NJ: Prentice Hall, 99. [].-. won, A. amhankar and. R. Rao, Overview of H.264/MPEG-4 part, J. Vis. Commun. mage R., vol. 7, pp. 6-26, April 26.