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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Delta-function
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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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Convolution

• 1D and 2D signal processing

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Consider the delta function
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Time-shift delta
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Sample the input (its a convolution!)
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What does sampling do to spectrum?
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What is the spectrum?
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Fourier Coefficients
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CTFT
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Eulers identity
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Sine-cos Rep
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Harmonic Analysis
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Convolutiontime-shiftmulti
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Convolution Thm
multiplication in the time domain convolution
in the frequency domain
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Sample
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Spectrum reproduced
spectrum to be reproduced at intervals
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Summary
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Example of 1D convoln
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2D Convolution
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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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Chapter 9

• Spatial Filters
• Blurring
• Median Filtering
• Hi-pass filtering
• SpatialFilterFrame and JAI

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BlurringLow-pass Filters
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Why Blur an Image?

• Remove Noise
• Other ideas?

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Averagelow-pass
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Want Unity Gain
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Many variations on LP filters
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Gaussian Blur
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Why use Gaussian Blur?

• How the eye works
• Symmetric
• Differentiable
• Smooth

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Classic bell curve
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Larger Kernelsmore blur
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Median Filtering

• Middle of a list of samples listed in ascending
  order.
• Sort samples, return n/2

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Why use median filtering?

• Discard outliers
• 0, 85, 90, 87 and 100. The mean is 72
• Median is 87.
• 0, 85, 87, 90, and 10087

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How do I implement the median?
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Salt and Pepper
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Median 3x3
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Median on any kernel
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Median result
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Median Octagon, less aggressive
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Median Octagon results
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Median Filtering is not FREE!

• Image degradation
• Selective median filtering.
• How do you know when to apply it?