EECS490: Digital Image Processing. Lecture #11

Transcription

1 Lecture #11 Filtering Applications: OCR, scanning Highpass filters Laplacian in the frequency domain Image enhancement using highpass filters Homomorphic filters Bandreject/bandpass/notch filters Correlation (revisited) Color basics (Chapter 6)

2 Filtering for OCR No filtering. Broken characters are difficult to recognize. Filtered with a GLPF with D 0 =80. Characters are fuller and filled in.

3 Filtering for Fun and Profit Removes wrinkles around eyes.

4 Filtering to Remove Scan Lines

5 Highpass Filters (Frequency Domain)

6 Highpass Filters (Spatial Domain) n=2 Gaussian shows no ringing.

7 Test Image: Ideal HPF H( u,v)= 0 if D ( u,v ) D 0 1 if D( u,v)> D 0

8 Test Image: Butterworth HPF H( u,v)= D 0 Du,v ( ) 2n

9 Test Image: Gaussian HPF H( u,v)= 1 e ( u,v) 2 2 D 0 D 2

10 HPF Mathematical Definitions

11 Laplacian Frequency Domain Filter F 2 f( x, y) x 2 ( ) + 2 f x, y y 2 = ( ju) 2 Fu,v ( )+ ( jv) 2 Fu,v ( ) F { 2 f( x, y) }= ( u 2 + v 2 )Fu,v ( ) (0,0) Note that the inverse Fourier transform of this filer is x-y oriented (no diagonals).

12 HPF for Edge Detection ( ) D 2 u,v Highpass filtering using a Butterworth filter to enhance ridges (high frequencies) and reduce effects of smudging (low frequencies). Since highpass filtering darkens the image thresholding is used to enhance the ridges.

13 HPF Image Enhancement Unsharp masking f s ( x, y)= f( x, y) f ( x, y) ( u,v)= 1 H lp ( u,v) H hp g( x, y)= f( x, y) 2 f x, y H ( u,v )= 1 u M 2 Sharpening 2 ( ) + v N 2 2

14 High-Frequency Emphasis H hb H hfe ( u,v)= ( A 1)+ H hp ( u,v) ( u,v)= a + bh hp ( u,v) Gaussian highpass filtering High-frequency emphasis using same filter Histogram equalized

15 f( x, y)= i( x, y)r( x, y) EECS490: Digital Image Processing Theory of Homomorphic Filtering z( x, y)= ln( f( x, y) )= lni( x, y)+ ln r x, y F z( x, y) ( ) { }= F { lni( x, y) }+ F ln r x, y Z( u,v)= F i ( u,v)+ F r ( u,v) { ( )} Su,v ( )= H( u,v)z( u,v)= H( u,v)f i ( u,v)+ H( u,v)f r ( u,v) s( x, y)= i' ( x, y)+ r '( x, y) g( x, y)= e sx,y ( ) = e i '( x,y) e r '( x,y) = i o ( x, y)r o ( x, y) Separate image into incident (low frequency) and reflected (high frequency) components Use log to separate frequency components Fourier transform high and low frequency components s( x, y)= F 1 { Su,v ( )}= F 1 { H( u,v)f i ( u,v) }+ F 1 H( u,v)f r u,v Filter components Exponentiate to re-combine { ( )} Inverse transform

16 Homomorphic Filtering Fourier transform and process high and low frequency components differently ( ) 1 e c H( u,v)= H L D 2 ( u,v) D 0 2 H >1 + L L <1 c controls smoothness

17 Homomorphic Filtering

18 Homomorphic Filtering Reduce effects of low frequency hot spots

19 Bandreject Filters

20 Bandreject/Bandpass Filters Bandreject Bandpass

21 Notch Filtering to Remove Periodic Noise Frequency components (moire) due to halftone printing grid and scanning grid Butterworth notches to remove moire effects

22 Notch Filtering Strong periodic noise in y-direction Image corrupted with 60Hz hum v-axis notch filter to remove periodic noise on vertical axis

23 Notch Filtering Convert the notch (reject) filter to a notch pass (invert it), filter the image, and inverse Fourier transform to reveal the nature of the noise.

24 FFT vs DFT Computational Advantage For large images you always want to use an FFT due to its large computational advantage.

25 Ch12 Object Recognition

26 Correlation Convolution f 2 Correlation f 2 M 1 i=0 N 1 j =0 ( m,n)= f 1 i, j M 1 i=0 N 1 j =0 ( ) ( m,n)= f 1 i, j ( ) ( ) hm i,n j ( ) hm+ i,n + j

27 How to find objects of interest in an image Define an Euclidian distance d 2 (y) d 2 2 ( y)= f ( x) t ( x y) = f 2 ( x) 2 f ( x)t ( x y)+ t ( 2 x y) x x The first term can be nearly constant depending upon the spatial uniformity of the image The second term is the cross correlation function The third term is the energy of the template, a constant. f( x, y) t( x, y)

28 False errors from correlation Noisy object Large noise spike

29 Normalize to prevent false responses Images to be matched Patches to be matched f 1 ( ) ( x) f 2 x q 1 q 2 Variances 2 ( q 1 )= E( q 1 ) E 2 2 ( q 1 ) ( q 2 )= E( q 2 ) E 2 ( q 2 ) Normalized correlation N ( y)= E ( qq 1 2 ) E( q 1 )E q 2 ( q 1 ) ( q 2 ) ( ) Typically we can think of q 1 as the template, i.e., all of f 1, and q 2 the section of f 2 covered by the displaced q 1

30 Sequential Similarity Detection Algorithm Correlation ab ( y)= a ( ij x) b ij x y If a and b are highly correlated, this summation will be essentially all 1 s yielding a large result. Threshold this summation after say 10 terms. If this sum is less than T (the threshold) it is probably uncorrelated and the summation will stop. i, j ( )

31 Moravec Interest Operator (produce candidate interest points based upon image activity) Define the variance operator Var( x)= Var( x, y)= f( x, y) f x+ k, y + l k,lins The region S is a local region defined to fit the application. Algorithm: 1. Find the local minimum of the variance IntOpVal( x):= min Var( x + y) y 1 2. Find local maxima 3. Interesting point if ( ) IntOpVal( x):= 0 unless IntOpVal( x) IntOpVal x + y IntOpVal( x)> T 2 Interest is minimum of variance in some small region ( ) for y 1 Nonzero only if the activity is a local maximum Threshold to get really interesting points

32 White Light A prism splits white light into its component colors.

33 Optical Units Radiometric units: Radiance (watts/sr/m 2 ) total energy emitted by a light source Irradiance (watts/m 2 ) total energy incident on a surface source Photometric units: Luminous flux (lumens) similar to radiance except corrected for wavelength sensitivity of the human eye Candela power emitted by a light source in a particular direction corrected for wavelength sensitivity of the human eye Luminance (candela/m2) incoming energy as measured by a detector

34 Human Eye The cones provide all the color sensitivity and are concentrated near the macula. Relative color sensitivity of the cones. 65% of cones are red sensitive; 33% are green sensitive; 2% are blue sensitive.

35 Primary/Secondary Colors (Primary) additive colors operate in transmission such as found in televisions and computer monitors RGB (Secondary) subtractive colors operate in reflection such as found in printing For example, yellow absorbs blue and reflects red+green=yellow CMY Subtractive colors operate by absorbing a primary color. They usually require black.