Computing for Engineers in Python

Transcription

1 Computing for Engineers in Python Lecture 10: Signal (Image) Processing Autumn Some slides incorporated from Benny Chor s course 1

2 Lecture 9: Highlights Sorting, searching and time complexity Preprocessing (sorting) the data enables fast (O(log 2 n)) access to what we are interested in (searching) Binary search algorithm + time complexity analysis Comparing recursive vs. iterative implementations efficiency Bubble sort + time complexity analysis Is there a faster sorting algorithm? Yes! (Quick Sort in tirgul) Comparing Bubble sort to sorted efficiency Generic sorting 2

3 More Sorting Algorithms Insertion, Selection O(n 2 ) in tirgul Quick sort O(nlog 2 n) on average in tirgul Average versus worst case analysis week) (maybe next "בהזדמנות " Merge sort O(nlog 2 n) worst case Can we do better than O(nlog 2 n) in general? Bucket sort 3

4 Signal Processing In the physical world, any quantity measurable through time or over space can be taken as a signal Signals are or electrical representations of timevarying or spatial-varying physical quantities Signal processing: applying mathematical techniques for the extraction, transformation and interpretation of signals, in either discrete (digital) or continuous (analog) time Example signals: radio, telephone, radar, sound, images, video, sensor data 4

5 Digital Images Digital image is a numeric representation of a two-dimensional image Examples: photos, microscopic, medical, astronomical 5

6 Image Representation Encoded as a n-by-m matrix M Each element M[x,y] in an image is called picture element (pixel), representing the light intensity / color at that location RGB, gray-level images Video an image for each time t 6

7 Resolution Pixel resolution vs. spatial resolution Pixel resolution == pixel count depends on properties of the system creating the image, not just the pixel resolution Same number of pixels, different spatial resolution: 7

8 Image Quantization Number of bits per pixel 24 bit RGB 16 colors Note that both images have the same pixel & spatial resolution

9 Gray Level Images The remaining of class will deal with gray-level images (although can be applicable for color images) 8 bits per pixel (256 gray levels), 0 black, 255 white Other representations: Binary 1bit per pixel Some applications use more colors (medical imaging) 9

10 An Example 10

11 Image Processing Signal processing for which the input is an image Typical operations: Color corrections / calibration Image segmentation Image registration / alignment Denoising Typical applications: Machine vision Medical image processing Face detection Augmented reality 11

12 In Python How to handle an image? The Python Imaging Library Example tutorial: The Image Module: Capacities: Read / write images Display image Basic image processing 12

13 Loading and Viewing an Image 13

14 Access Pixels 14

15 Create and Save an Image 15

16 Output 16

17 Rolling an Image 17

18 Output 18

19 Rotating an Image 19

20 Edges Sharp change in intensity between close pixels Denoted edges Usually captures much of the meaningful information in the image Edge detection algortihms: Sobel Lena Laplacian 20

21 Edge Detection Example 21

22 Blur and Noise Gaussian blur (sigma = 2) Gaussian noise Lena Salt and pepper noise Credit: Wikipedia 22

23 Denoising Algorithms Examples: Local means: replace observed pixel with neighborhood s (usually 3x3 mask) average Local medians: with neighborhood s median x 23

24 Denoising Algorithms Local means: Pros: reduces noise on smooth areas Cons: blur edges, sensitivity to extreme values (e.g., as in salt and pepper noise) Local medians: Pros: preserve edges, not sensitive to extreme values Cons: eliminate fine details (contours) in the image x 24

25 Example In Tirgul 25

26 Image Manipulation Full Example 26

27 Image Segmentation 27

28 Image Segmentation Algorithms Thersholding Clustering Region growing Compression-based methods Histogram-based methods Model-based methods Etc. 28

29 Thresholding Simplest segmentation method Apply a threshold to turn a gray-scale image into a binary image The key is to select the appropriate threshold value Popular method Otsu s method (maximal variance) 29

30 Example - Thresholding 30

31 Example - Thresholding 31

32 Results TH = 20 TH = 80 TH = 140 TH =

33 HW The Whole Loop Input: noisy image Output: segmented contours on top of input image How? Denoising Edge detection Thresholding (histogram based Otsu s algorithm) Visualization 33

34 Real World Application Face Detection Credit: Intel Technology Journal, Volume 09, Issue 01 34

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