Filtering and Enhancing Images

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

Why? Improvement Improvement Low level feature detection Low level feature detection

Definitions Image enhancement = improve the detectability of important features Image enhancement = improve the detectability of important features –Noise reduction –Smoothing –Contrast enhancement –Edge detection

Noise reduction example

Contrast enhancement example

Definitions Image restoration = restore degraded image Image restoration = restore degraded image –Usually needs a model of degradation

Image restoration examples (deconvolution)

POINT OPERATIONS

Definitions Point operation = output pixel is determined only by the input pixel Point operation = output pixel is determined only by the input pixel –Out[x,y] = f(In[x,y]) Contrast stretching = point operator that uses a piecewise smooth function of the input gray value to enhance important details of the image. 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? What are some examples that we have already seen?

Examples of point operations: Threshold (demo) Threshold (demo) Invert (demo) Invert (demo) Out[x,y] = max – In[x,y] RGB  gray conversion RGB  gray conversion Gamma correction Gamma correction

Gamma correction example

NEIGHBORHOOD OPERATIONS

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

Image smoothing Gaussian filter Gaussian filter

Lowpass (smoothing) filter example

Highpass filter example

Image smoothing Median filter (or more generally, order statistic or filter) Median filter (or more generally, order statistic or filter)

Median filter example

RECALL FROM A PREVIOUS DISCUSSION (HOLE AND OBJECT COUNTING)...

Masks

Mask = set of pixel positions and corresponding values called weights Mask = set of pixel positions and corresponding values called weights Mask origin = usually center Mask origin = usually center How? How? 1.Calculate sum of products Boundary Boundary 1.Replicate nearest pixel value 2.Use 0 2.Normalize or clamp (or an amplitude shift will occur) Applying masks to images

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

Convolution See for some nice animations. See for some nice animations.

1*40+2*40+1*80+ 2*40+4*40+2*80+ 1*40+2*40+1*80 =800

1*40+2*80+1*80+ 2*40+4*80+2*80+ 1*40+2*80+1*80 =1120

But what about borders? When we are missing data at the edges, we typically do one of the following: When we are missing data at the edges, we typically do one of the following: 1.Copy to the missing value, the nearest neighboring value. 2.Use 0 for the missing value(s). (Regardless, it really doesn’t matter, but we need to consistently do something.)

1*40+2*40+1*40+ 2*40+4*40+2*40+ 1*40+2*40+1*40 =640 Method 1: copy nearest

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

=16 640/16