Local Enhancement. Local enhancement
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1 Local Enhancement Local Enhancement Median filtering (see notes/slides, 3.5.2) HW4 due next Wednesday Required Reading: Sections 3.3, 3.4, 3.5, 3.6, 3.7 Local Enhancement 1 Local enhancement Sometimes Local Enhancement is Preferred. Malab: BlkProc operation for block processing. Left: original tire image. Local Enhancement 2
2 Histogram equalized Local Enhancement 3 Local histogram equalized F=@ histeq; I=imread( tire.tif ); J=blkproc(I,[20 20], F); Local Enhancement 4
3 Fig 3.23: Another example Local Enhancement 5 Local Contrast Enhancement Enhancing local contrast g (x,y) = A( x,y ) [ f (x,y) - m (x,y) ] + m (x,y) A (x,y) = k M / σ(x,y) 0 < k < 1 M : Global mean m (x,y), σ (x,y) : Local mean and standard dev. Areas with low contrast Larger gain A (x,y) (fig ) Local Enhancement 6
4 Fig 3.24 Local Enhancement 7 Fig 3.25 Local Enhancement 8
5 Fig 3.26 Local Enhancement 9 Image Subtraction g (x,y) = f (x,y) - h (x,y) h(x,y) a low pass filtered version of f(x,y). Application in medical imaging -- mask mode radiography H(x,y) is the mask, e.g., an X-ray image of part of a body; f(x,y) incoming image after injecting a contrast medium. Local Enhancement 10
6 Subtraction: an example Local Enhancement 11 Fig 3.28: mask mode radiography Local Enhancement 12
7 Averaging g( x, y) = f ( x, y) + #( x, y) M 1 g( x, y) = " M g x y i (, ) E( g( x, y)) = f ( x, y) and $ g = $ # ( x, y) M #( x, y)! Uncorrelated zero mean $ 2 # i= 1 ( x, y)! Re duces the noise variance Fig 3.30 Local Enhancement 13 Fig 3.30 Local Enhancement 14
8 Another example Images with additive Gausian Noise; Independent Samples. I=imnoise(J, Gaussian ); Local Enhancement 15 Averaged image Left: averaged image (10 samples); Right: original image Local Enhancement 16
9 Spatial filtering Frequency LPF HPF BPF Spatial 0 Local Enhancement 17 Smoothing (Low Pass) Filtering f 1 f 2 f 3 ω 1 ω 2 ω 3 ω 4 ω 5 ω 6 ω 7 ω 8 ω 9 (x,y) Replace f (x,y) with ^ f ( x, y ) =!" f i i i Linear filter LPF: reduces additive noise blurs the image sharpness details are lost (Example: Local averaging) Fig 3.35 Local Enhancement 18
10 Fig 3.35: smoothing Local Enhancement 19 Fig 3.36: another example Local Enhancement 20
11 Image Dithering Dithering: to produce visually pleasing signals from heavily quantized data. Halftoning: convert a gray scale image to a binary image by thresholding. Dithering to add noise so that the resulting image is smoother than just thresholding (but still it is a binary image) Your homework #4 explores this further with a MATLAB exercise. Local Enhancement 21 Median filtering Replace f (x,y) with median [ f (x, y ) ] (x, y ) E neighbourhood Useful in eliminating intensity spikes. ( salt & pepper noise) Better at preserving edges. Example: Median=20 ( 10,15,20,20,20,20,20,25,100) So replace (15) with (20) Local Enhancement 22
12 Median Filter: Root Signal Repeated applications of median filter to a signal results in an invariant signal called the root signal. A root signal is invariant to further application of the medina filter. Example: 1-D signal: Median filter length = root signal Local Enhancement 23 Invariant Signals Invariant signals to a median filter: Constant Monotonically increasing decreasing length? Local Enhancement 24
13 Fig 3.37: Median Filtering example Local Enhancement 25 Media Filter: another example Original and with salt & pepper noise imnoise(image, salt & pepper ); Local Enhancement 26
14 Donoised images Local averaging K=filter2(fspecial( average,3),image)/255. Median filtered L=medfil2(image, [3 3]); Local Enhancement 27 Sharpening Filters Enhance finer image details (such as edges) Detect region /object boundaries. Example: Local Enhancement 28
15 Edges (Fig 3.38) Local Enhancement 29 Unsharp Masking Subtract Low pass filtered version from the original emphasizes high frequency information I = A ( Original) - Low pass HP = O - LP A > 1 I = ( A - 1 ) O + HP A = 1 => I = HP A > 1 => LF components added back. Local Enhancement 30
16 Fig 3.43 example of unsharp masking Local Enhancement 31 Derivative Filters 1/ ω #!f = % " f $ "x Gradient " f "y #) " f,!f = % * + "x -. $ % 2 & ( ' T ) + " f, * + "y -. 2 & ( '( 1 2 Local Enhancement 32
17 Edge Detection Gradient based methods #!f = " f $ % "x " f & "y ' ( T f(x) f (x) f (x) f(x) x 0 x x 0 f (x) f (x) d(.)/dx. Threshold < Not an edge x > Local max No Local Enhancement 33 x 0 X 0 not an edge x Yes X0 is an edge Digital edge detectors z 2 z 1 z 3 z 4 z 5 z 6 z 7 z 8 z 9 ( ) 2 + ( z 5 # z 6 ) 2!f " $ z 5 # z % 8!f " z 5 # z 8 + z 5 # z & ' Robert s operator z 5 -z 9 z 6 -z prewitt Sobel s Local Enhancement 34
18 Fig 3.45: Sobel edge detector Local Enhancement 35 Laplacian based edge detectors 2 2 " f! f = + 2 " x " " 2 f 2 y Rotationally symmetric, linear operator Check for the zero crossings to detect edges Second derivatives => sensitive to noise. Local Enhancement 36
19 Fig 3.40: an example Local Enhancement 37
Local enhancement. Local Enhancement. Local histogram equalized. Histogram equalized. Local Contrast Enhancement. Fig 3.23: Another example
Local enhancement Local Enhancement Median filtering Local Enhancement Sometimes Local Enhancement is Preferred. Malab: BlkProc operation for block processing. Left: original tire image. 0/07/00 Local
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