ENDS 375

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ENDS 375

• Foundations of Visualization
• 9/9/04 Notes

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Geometric Operations

• Scaling - changing x,y size
• Rotation - rotation about a point
• Translation - shift image
• Operation ordering important

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Sampling

• Creating a new image based on sub-pixel
  information from the original image
• Needed for most geometric operations

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Sampling

• Forward Transformation
• from source to destination
• Inverse Transformation
• from destination to source

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Sampling

• Nearest Neighbor

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Bilinear Interpolation
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Warping

• Polynomial warping
• Morphing

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Frequency Domain
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Image information changes
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1-Dimensional Example

• Single row of pixels
• represent a continuous signal
• think of the signal as made up of combined sine
  and cosine functions having various frequencies
  and relative phases

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Changes in both x and y
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Frequency Domain Operations

• Frequency Domain
• Fourier Transform
• Power Spectra
• Inverse Fourier

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FFT Example

• Fast Fourier Transform

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File Formats

• Many variations on a theme
• File Headers
• Compression techniques

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Image File Storage

• plane sequential
• row sequential
• pixel or point sequential

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Image Compression

• lossless
• lossy
• Compression Ratios

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Compression Techniques

• Run-Length Encoding
• Huffman Encoding
• Statistical, used for Faxes
• LZW Compression - GIF
• JPEG, ...

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RLE Encoding

• Uses image pixel redundancy
• Encodes runs of identical pixel values
• Uses Counts and Values
• SGI Implementation - Tables

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JPEG

• 8 x 8 pixel blocks
• Uses Discrete Cosine Transforms (DCT)
• related to Discrete Fourier

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JPEG Steps

• Calculate DCTs
• Coefficient Quantization
• choose the quality level (and compression ratio)
• Encode results
• Huffman encode the quantized data
• DPCM encode dc coefficients
• 201 compression not unusual

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Readings

• Course notes section 1-10
• optional
• Course notes section 1-11
• Course notes section 1-12
• Textbook - Chapter 14