Digital filters. Remote Sensing (GRS-20306)

Transcription

1 Digital filters Remote Sensing (GRS-20306)

2 Digital filters Purpose Operator Examples Properties (L&K pp and section 7.5)

3 Digital filters and RS images Local operation by "mask" or "window" or "template" with some algorithm ("kernel") Purposes: Image improvement or restoration - elimination of disturbances in points and/or lines - noise suppression - image enhancement (sharpening) - edge detection of line structures preprocessing before spectral classification - averaging of field units - elimination of local disturbances discover spatial patterns (enhancement) - distinguish area, line and point objects through window operations

4 E.g. 3 x 3 filter window: h(r,s) stepwise moving window (per pixel) ƒ(x,y) x image matrix y Input to algorithm: 9 pixel values from the input image Output to central pixel: 1 filter result value in the output image

5 Filter Definition Filter: operation scheme (mask) h(r,s), which moves over the image ƒ(x,y). size mask = N N window pixel to pixel transformation neighbourhood dependent (local operator) the central pixel value is replaced by the filter result the window moves pixel by pixel, line by line across the image 2 classes of filter operators: linear filters non-linear filters

6 Operation of Digital Filters s x y r ƒ(x,y) = image pixel value as a function of position (in original image) The concept convolution is used with linear filtering: g(x,y) = ƒ(x,y) h(r,s) filter result operation scheme x,y: central window coordinates in the image to be filtered ƒ(x,y) r,s: number of steps relative to the centre, that is to say the coordinates r or s N = 3: N = 5: N = size of the window N = 7: (preferably odd)

7 Examples h(r,s) with N = 3: 1/9 * Low pass filter (moving average) ƒ(x,y) x y shows long periodic fluctuations trends

8 High pass filter 1/9 * High pass filter ƒ(x,y) x y shows short periodic fluctuations local transitions Low pass + high pass = original image!!

9 Example TM image, band 5

10 Result low pass filter, 3x3 window

11 Result high pass filter, 3x3 window

12 Gradient filter first derivative of ƒ(x,y) in a chosen direction dƒ clear edge dƒ / dx large weak edge dƒ / dx small dx One may consider this as a 3 3 convolution: ; also (45º): etc

13 Laplace filter d 2 ƒ / dx 2 : second derivative of ƒ(x,y) in x ànd y directions simultaneously f 1 f 2 f 3 f 2 - f 1 f 3 - f 2 òr f 1 - f 2 f 2 - f 3 (f 2 - f 1 ) - (f 3 f 2 ) (f 2 - f 3 ) - (f 1 - f 2 ) = - f f 2 - f 3 = - f f 2 - f 3 = d 2 ƒ / dx 2 = d 2 ƒ / dx 2 Filter operation scheme: -1 2 and (-1 2-1) together. -1

14 Horizontal gradient filter Horizontal gradient filter first derivative x direction ƒ(x,y) x y

15 Vertical gradient filter Vertical gradient filter first derivative y direction ƒ(x,y) x y

16 Horizontal Laplace filter Horizontal Laplace filter ƒ(x,y) x y

17 Vertical Laplace filter Vertical Laplace filter ƒ(x,y) x y

18 Laplace filter (-1 2-1) with 2 gives Laplace Blurred image (original) + Laplace filter Sharper image =

19 Example TM image, band 5

20 Result Laplace + original, 3x3 window

21 Result vertical gradient filter, 3x3 window

22 Edge Detection R: Sobel filter filter value = (R 2 + S 2 ) x y and S: x The direction of the edge is: arctan (S/R) y

23 Example Sobel filtering

24 Example Sobel filtering

25 Median filter E.g.: ƒ 1 ƒ 2 ƒ ƒ 4 ƒ 5 ƒ ƒ 7 ƒ 8 ƒ Median filter: the 9 pixel values are ordered ƒ 6 ƒ 2 ƒ 3 ƒ 7 ƒ 4 ƒ 1 ƒ 8 ƒ 9 ƒ 5 pixel value ƒ 4 is now assigned to the central pixel

26 Properties of Filters Linear filters Low pass: averaging small fluctuations in image values; random noise suppression; smoothing however: image fading (blurring) High pass: enhancing details (also noise); emphasizing edges Gradient: directional filter for line structures Laplace: improving image sharpness, (+ original) enhancing details

27 Properties of Filters -2- Non-Linear filters Median: suppressing isolated noise or peaks; preserving edges however: rounding off corners of fields Prewitt Sobel : edge detectors; Kirsch exaggerate edges even

28 Example Median filtering

29 New filtering techniques Fourier analysis: spatial frequency decomposition Wavelet analysis Kalman filter: recursive filter which estimates the state of a dynamic system from a series of incomplete and noisy measurements

30 Spatial aggregation Dutch land use data base (LGN) 25 m + 39 classes aggregated to 300 m + 9 classes

31 Questions???