CS 490: Computer Vision Image Segmentation: Thresholding. Fall 2015 Dr. Michael J. Reale

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1 CS 490: Computer Vision Image Segmentation: Thresholding Fall 205 Dr. Michael J. Reale

2 FUNDAMENTALS

3 Introduction Before we talked about edge-based segmentation Now, we will discuss a form of regionbased segmentation, thresholding

4 Basic Thresholding fx,y = input image T = threshold gx,y = output binary image g x, y 0 if if f f x, y x, y T T If gx,y == object point Otherwise background point

5 Types of Thresholding Two basic types of thresholding: Global thresholding Same value of T across entire image Variable thresholding Value of T changes over image

6 Variable Thresholding Local or regional thresholding T changes depending on properties of neighborhood of x,y E.g., average intensity in neighborhood Dynamic or adaptive thresholding T changes based on spatial coordinates x,y

7 Multiple Thresholding Maybe you are looking for two different kinds of objects, each with a different general intensity Can try to use multiple thresholding: However, very difficult to segment objects correctly with two thresholds 2 2, if, if, if, T y x f c T y x f T b T y x f a y x g

8 Thresholding and Histograms Modes highest points of intensity histogram indicative of how you want to split intensity Success of segmentation through thresholding dependent on: Separate between peaks/modes More separation better segmentation 2 Noise content in image Noise broadens the modes 3 Relative sizes of objects and background 4 Uniformity of illumination source If lighting changes across image problems with picking a good threshold 5 Uniformity of reflectance properties of the image Similar to lighting issue, except it refers to the objects

9 Picking a Global Threshold Can use iterative approach: Select estimate of global threshold T Usually start with average intensity 2 Segment image using T produces two groups G and G 2 one above and one below the threshold 3 Compute average mean intensity values m and m 2 for pixels in G and G 2 4 Compute new threshold value: T 2 m m 2 5 Repeat steps through 4 until difference between successive T values is less than ΔT Larger ΔT faster

10 OPTIMUM GLOBAL THRESHOLDING USING OTSU S METHOD

11 Introduction Can look at thresholding as classification problem Assign pixels to one of two classes while minimizing error Otsu s method approaches thresholding with this in mind Optimum maximizes between-class variance

12 Otsu s Method Compute normalize histogram of image each component is p i 2 Compute cumulative sums, P k, for all k all intensity levels Threshold splits pixels into two classes P k and P 2 k probabilities of a pixel being in that class 3 Compute cumulative means, mk, for all k intensity levels 4 Compute global intensity mean, m G 2 0 k P p k P p k P L k i i k i i k i ip i k m 0 0 L i m G ip i

13 Otsu s Method 5 Compute between-class variance σ 2 Bk for all k k 2 B 6 Obtain the Otsu threshold, k*, as value of k for which σ 2 Bk is maximum Cycle through all intensity values until you find the best one If maximum not unique get average of all k values that correspond to the maxima detected 7 Obtain separability measure η* for k* Gives idea of how easy it is to threshold image Value between [0,] 0 = all pixels have same intensity = only two intensities, 0 and L- mg P k m k P k P k 2 2 B k k 2 G 8 Threshold image with k*

14 Otsu s Method Example

15 IMPROVING GLOBAL THRESHOLDING

16 Smoothing Noise flattens histogram Can also make multimodal histogram unimodal Smoothing can reduce noise and improve thresholding However, depends on scale of regions Too small drowned out by noise

17 Example Where Smoothing Helps Smoothing causes separation of peaks in histogram better segmentation

18 Example Where Smoothing Does Not Help Smoothing applied in bottom row, but does not alter histogram Region we want is too small

19 Edges Using edge information i.e., gradient or Laplacian values instead of intensity directly can improve thresholding Compute edge image 2 Threshold edge image g T x,y Use as mask image in next step T usually set fairly high 90 th percentile 3 Compute histogram from pixels in fx,y that have value of in g T x,y 4 Use histogram to segment fx,y globally E.g., using Otsu s method

20 Example of Using Edges to Improve Thresholding a Noisy image b histogram c gradient image d Product of a and c e histogram f thresholded image

21 VARIABLE THRESHOLDING

22 Image Partitioning Subdivide image into non-overlapping rectangles Helps overcome non-uniform illumination and/or reflectance Choose subimage size small enough that illumination inside subimage is uniform Apply threshold-finding algorithm to each subimage Problem: If subimage contains only object or background pixels thresholding fails

23 Variable Thresholding Based on Local Image Properties Select threshold for each pixel x,y based on its neighborhood Example: use mean and std. dev. Given a,b = non-negative constants Values usually determined experimentally Using local mean and std. dev.: T xy a Using global mean and local std. dev.: T xy a xy xy bm bm xy G

24 Moving Averages Compute moving average along scan lines of an image If: Very useful in document processing z k+ = intensity of point in scanning sequence at step k+ N = # of points in scan line to use for average m = z /n pretends border is padded with zeros Then moving average m: k m k zi m k zk n n ik 2n z k n Threshold given by: b = constant Txy bm xy

25 Example of Moving Averages Thresholding Original Otsu s Method Moving Averages

26 MULTIVARIABLE THRESHOLDING

27 Multivariable Thresholding Example: color segmentation! 3 values RGB Can use distance function and threshold if distance too great: Example: spherical Example: covariance matrix of samples /, B B G G R R T a z a z a z a z a z a z a z D 2 /, a z C a z a z D T