Digital Image Processing Fundamentals

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Chapter 5

• Digital Image Processing Fundamentals

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Learning Goals

• The human visual system
• Digitizing images
• Display of Images

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Trading an eye for an ear
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An eye is a Multi-mega pixel camera

• It has a lens (adjustable zoom)
• It has an automatic f-stop (iris 2-8 mm)
• It has a sensor plane (100 million pixels)
• The sensor has a transfer function senstive to
  mesopic range 380 to about 700 nm

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The eyes have a USB2 data rate!

• 250,000 neurons in the optic nerve
• variable voltage output on EACH nerve
• 17.5 million neural samples per second
• 12.8 bits per sample
• 224 Mbps, per eye (a 1/2 G bps system!).
• Compression using lateral inhibition between the
  retinal neurons

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Response curves

• Eye has Gaussian response to light.
• Gives rise to biologically motivated image
  processing

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Quantization of an Image

• Computers use digital cameras -gt quantization

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Sampling an Image
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Samplingconvolution w pulse train
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Quantization Error is visible
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Displays

• Color Monitors are made for people

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Chapter 6-7

• Opening and Saving Images

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Chapter 8 Convolutionwith a kernel, g(x)
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Region of Support

• The region of support is defined as that area of
  the .kernel which is non-zero
• linear convolutionsignal has infinite extent
  but kernel has finite support
• If function has finite region of support we have
  compact support

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Real images have finite region of support

• But we treat them as periodic and infinite!
• We repeat kernels so that they have the same
  period as the images.
• We call this cyclic convolution.

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Convolution in 2D
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Avoid the Mod op
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What is wrong with avoiding the mod op?

• How do I find the center of the kernel?

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Cyclic Convolution
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Implementing Convolution
for(int y 0 y lt height y) for(int
x 0 x lt width x) sum 0.0
for(int v -vc v lt vc v)
for(int u -uc u lt uc u)
sum fcx(x-u) cy(y-v) k uucvvc
if (sum lt 0) sum 0 if (sum gt 255)
sum 255 hxy (short)sum

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What happens to the image if you ignore the wrap?
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Cyclic Convolution keeps the edges

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Can you think of a better way to implement
convolution?

• Keep the edges!
• Dont use the mod operation.
• How about growing the image by the size of the
  kernel2?

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Convolution is slow, how can I speed it up?

• JAI!
• FFT!?
• Other ideas?

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