Filtering and Enhancing Images

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Filtering and Enhancing Images
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Major operations

1. Matching an image neighborhood with a pattern or
   mask
2. Convolution (FIR filtering)

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Why?

• Improvement
• Low level feature detection

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Definitions

• Image enhancement improve the detectability of
  important features
• Noise reduction
• Smoothing
• Contrast enhancement
• Edge detection

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Noise reduction example
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Contrast enhancement example
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Definitions

• Image restoration restore degraded image
• Usually needs a model of degradation

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Image restoration examples (deconvolution)
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Point operations
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Definitions

• Point operation output pixel is determined only
  by the input pixel
• Outx,y f(Inx,y)
• Contrast stretching point operator that uses a
  piecewise smooth function of the input gray value
  to enhance important details of the image.
• What are some examples that we have already seen?

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Examples of point operations

• Threshold (demo)
• Invert (demo)
• Outx,y max Inx,y
• RGB ? gray conversion
• Gamma correction

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Gamma correction example
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Neighborhood operations
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Image smoothing

• Neighborhood operations require more than a
  single image point
• Box filter smoothing via equally weighted
  rectangular neighborhood (mask)

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Image smoothing

• Gaussian filter

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Lowpass (smoothing) filter example
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Highpass filter example
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Image smoothing

• Median filter (or more generally, order statistic
  or filter)

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Median filter example
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Recall from a previous discussion (hole and
object counting) . . .
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Masks
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Applying masks to images

• Mask set of pixel positions and corresponding
  values called weights
• Mask origin usually center
• How?
• Calculate sum of products
• Boundary
• Replicate nearest pixel value
• Use 0
• Normalize or clamp (or an amplitude shift will
  occur)

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Applying masks to images

• Derived from convolution
• Discrete form is cross correlation
• where f is the input image, h is the mask/filter
  kernel, and g is the output image result

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Convolution

• See http//en.wikipedia.org/wiki/Convolution for
  some nice animations.

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But what about borders?

• When we are missing data at the edges, we
  typically do one of the following
• Copy to the missing value, the nearest
  neighboring value.
• Use 0 for the missing value(s).
• (Regardless, it really doesnt matter, but we
  need to consistently do something.)

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Method 1 copy nearest
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The importance of normalizing or clamping the
result.

• Otherwise, the values might get larger and larger
  (brighter and brighter) or go out of the original
  range, depending on the filter.

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