Local enhancement. Local Enhancement. Local histogram equalized. Histogram equalized. Local Contrast Enhancement. Fig 3.23: Another example

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1 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 Enhancement 0/07/00 Local Enhancement Histogram equalized Local histogram equalized histeq; I=imread( tire.tif ); J=blkproc(I,[0 0], F); 0/07/00 Local Enhancement 3 0/07/00 Local Enhancement 4 Fig 3.3: Another example 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 < M : Global mean m (x,y), σ (x,y) : Local mean and standard dev. Areas with low contrast! Larger gain A (x,y) (fig ) 0/07/00 Local Enhancement 5 0/07/00 Local Enhancement 6

2 Fig 3.4 Fig 3.5 0/07/00 Local Enhancement 7 0/07/00 Local Enhancement 8 Fig 3.6 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. 0/07/00 Local Enhancement 9 0/07/00 Local Enhancement 0 Subtraction: an example Fig 3.8: mask mode radiography 0/07/00 Local Enhancement 0/07/00 Local Enhancement

3 Averaging Fig 3.30 g( x, y) = f ( x, y) + η( x, y) M gxy (, ) = M g x y i (, ) Egxy ( (, )) = f( xy, ) and σ g = σ η ( xy, ) M η( xy, ) Uncorrelated zero mean σ η i= ( xy, ) Reduces the noise variance Fig /07/00 Local Enhancement 3 0/07/00 Local Enhancement 4 Another example Images with additive Gausian Noise; Independent Samples. Averaged image I=imnoise(J, Gaussian ); Left: averaged image (0 samples); Right: original image 0/07/00 Local Enhancement 5 0/07/00 Local Enhancement 6 Spatial filtering Smoothing (Low Pass) Filtering Frequency LPF HPF BPF f f f 3 ω ω ω 3 ω 4 ω 5 ω 6 ω 7 ω 8 ω 9 (x,y) Replace f (x,y) with ^ f ( x, y )= ω f i i i Linear filter Spatial 0 LPF: reduces additive noise" blurs the image! sharpness details are lost (Example: Local averaging) Fig /07/00 Local Enhancement 7 0/07/00 Local Enhancement 8

4 Fig 3.35: smoothing Fig 3.36: another example 0/07/00 Local Enhancement 9 0/07/00 Local Enhancement 0 Median filtering Median Filter: Root Signal 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: ( 0,5,0,0,0,0,0,5,00) Median=0 So replace (5) with (0) 0/07/00 Local Enhancement 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: -D signal: Median filter length = root signal 0/07/00 Local Enhancement Invariant Signals Fig 3.37: Median Filtering example Invariant signals to a median filter: Constant Monotonically increasing decreasing length? 0/07/00 Local Enhancement 3 0/07/00 Local Enhancement 4

5 Media Filter: another example Donoised images Original and with salt & pepper noise imnoise(image, salt & pepper ); Local averaging K=filter(fspecial( average,3),image)/55. Median filtered L=medfil(image, [3 3]); 0/07/00 Local Enhancement 5 0/07/00 Local Enhancement 6 Sharpening Filters Edges (Fig 3.38) Enhance finer image details (such as edges) Detect region /object boundaries. Example: 8 0/07/00 Local Enhancement 7 0/07/00 Local Enhancement 8 Unsharp Masking Fig 3.43 example of unsharp masking Subtract Low pass filtered version from the original emphasizes high frequency information I = A ( Original) - Low pass HP = O - LP A > I = ( A - ) O + HP A = => I = HP A > => LF components added back. 0/07/00 Local Enhancement 9 0/07/00 Local Enhancement 30

6 Derivative Filters Edge Detection /9 ω Gradient L = N M T f f O f x y Q P L F = H G I K J F + H G f fi O f K J NM x y QP 0/07/00 Local Enhancement 3 Gradient based methods f(x) x 0 f(x) x No Not an edge 0/07/00 Local Enhancement X 0 not an edge 3 x 0 F f = H G f (x) f (x) f (x) d(.)/dx. Threshold < x f x f y > Local max I K J T x 0 f (x) x Yes X0 is an edge z z z 3 z 4 z 5 z 6 z 7 z 8 z 9 Robert s operator Digital edge detectors b 5 8g b 5 6g f z z + z z f z z + z z prewitt z 5 -z 9 z 6 -z 8 Sobel s /07/00 Local Enhancement 33 Fig 3.45: Sobel edge detector 0/07/00 Local Enhancement 34 Laplacian based edge detectors Fig 3.40: an example f f f = + x y -4 Rotationally symmetric, linear operator Check for the zero crossings to detect edges Second derivatives => sensitive to noise. 0/07/00 Local Enhancement 35 0/07/00 Local Enhancement 36