Notes 20110208 CIS 6320 Image Processing - Presentation 2 -- Mohommad Naeem
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Presentation 2 -- Discrete Cosine Transform -- Mohommad Naeem
- send report given instructions http://www.socs.uoguelph.ca/~matsakis/CIS6320/sched.htm
- talk about abstract items
- discuss frameworks
Contents |
Cosine Transform
- 1974 -- Ahmad, Rao and Nataranjan
- from Fourier Transform (FT) family ...
- closer to DFT -- but it only involves real numbers
- whereas FFT (fast Fourier transform) requires the use of complex numbers
- defined: forward transform in two dimensions and inverse transform
- properties that makes cosine transform very useful:
- decorrelation -- removes interpixel dependence
- energy compaction -- low level frequencies
- orthogonality -- no two cosine transforms can be written the same way
- separability -- 2D transform is equal to two 1D transforms
- real number arithmetic -- no complex values
- approches KLT -- in terms of compression, nearly obtains this level of optimality
Applications in DIP (digital image processing)
- key: image compression, watermarking, filtering
- additional: stenography, image coding ...
Digital Image Compression
- DCT is very good lossy compression
- JPEG adopted DCT
- lossy compression ratio up to 10:1
- used in many file formats
- Exif, Jfif etc.,
- the blocky effect is actual due to the quantization?
DCT Encoding
- image is broken up into 8x8 or 16x16 blocks
- as QL increases, we get a larger image
- entropy encoding is done by a zig-zag-diagonal-major pattern
- encoding (compression)
- color transform, down sampling, forward DCT, quantization, encoding
- results in JPEG compressed image
- decoding -- the opposite procedure using reverse DCT
Denoising and Restoration
- Block DCT (B-DCT)
- noise removal from regular shaped blockable regions
- handles stationary noise of a variety of types
- decorrelated non-stationary noise
- non-stationary: type unknown, statistical properties unknown
- SA-DCT
- irregular shaped regions
- state of the art denoising abilities
- process ...
- mean subtraction, SA-DCT, hard-thresholding, inverse SA-DCT, mean addition
- striking improvements from blurred or low quality images
Digital Watermarking
- digital signature in images
- required for copyright etc.,
- sensitive to compression, median filtering etc.,
- robust watermark ...
- resistant to attacks
- DCT effective against many attacks
- process ...
- original, divided image into blocks, image transform, watermark embedding, reverse transform, watermarked image
- missing one?
Digital Steganography
- hiding an image inside another image
Additional Applications
- image segmentation
- pattern recognition
- image resizing
- face recognition
- progressive image transmission
- image decomposing
- image decimation, interpolation
Uses
- MPEG compression as well
