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U of U ECE 6532 - What is image segmentation

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What is image segmentation? • Image segmentation is the process of subdividing an image into its constituent regions or objects. • Example segmentation with two regions: Input image intensities 0-255 Segmentation output 0 (background) 1 (foreground)Formal definition of segmentation • R: set of all pixels in given image • Segmentation into n regions R1,R2,...Rn • Two important properties – Complete – Mutually exclusiveTwo general approaches to segmentation • Discontinuity based – Partition an image based on abrupt changes of intensity. Find pixels which correspond to these abrupt changes, these will be the boundaries between regions. – Edge detection is an example of this type of approach to segmentation • Similarity based – Group pixels into regions of similar intensity – Thresholding is an example of this type of approach to segmentationGlobal thresholding • How can we choose T? – Trial and error – Use the histogram of f(x,y) Input image f(x,y) intensities 0-255 Segmentation output g(x,y) 0 (background) 1 (foreground)Role of noise T=120Low signal-to-noise ratio T=140When is global thresholding most useful? • The peaks in the histogram are well separated – Low noise, large signal-to-noise ratio • We saw earlier that we can solve this problem to some extent by smoothing the input image – The illumination over the image is close to uniform – The reflectance properties of the objects and the background are close to uniform • If the object (foreground) is much smaller in size than the background, the peak corresponding to the object might be hidden in a global histogram – Two possible solutions to this problem?When is global thresholding most useful? • The peaks in the histogram are well separated – Low noise, large signal-to-noise ratio • We saw earlier that we can solve this problem to some extent by smoothing the input image – The illumination over the image is close to uniform – The reflectance properties of the objects and the background are close to uniform • If the object (foreground) is much smaller in size than the background, the peak corresponding to the object might be hidden in a global histogram – Locally adaptive thresholding – Using edge information to limit the histogramForeground/background size disparity © 1992–2008 R. C. Gonzalez & R. E. WoodsUsing edge information © 1992–2008 R. C. Gonzalez & R. E. WoodsAnother example © 1992–2008 R. C. Gonzalez & R. E. WoodsLocal thresholding • One simple way – Subdivide image into blocks – Assumes every block has a portion of foreground and background © 1992–2008 R. C. Gonzalez & R. E. WoodsMoving mean • At every pixel (x,y) we can choose a threshold based on the mean m(x,y) of a local window • This is very useful for adapting to changes in illumination – Can be problematic if the window at (x,y) contains only foreground or only background – Can get around this problem by also using the standard deviation of the window: T = m(x,y) + aσ(x,y) © 1992–2008 R. C. Gonzalez & R. E. WoodsMoving mean - another example • At every pixel (x,y) we can choose a threshold based on the mean m(x,y) of a local window • This is very useful for adapting to changes in illumination – Can be problematic if the window at (x,y) contains onlt foreground or only background – Can get around this problem by also using thr standard deviation of the window: T = m(x,y) + aσ(x,y) © 1992–2008 R. C. Gonzalez & R. E. WoodsMultidimensional histograms • Sometimes we have multiple images of the same object – Different channels in multispectral data – Magnetic resonance images with different pulse sequences • Each channel provides new information • If we have two channels, we can create a 2D histogram A 2D histogram of a brain image from 2 MRI channelsClustering T2 PD T1 CSF WM GM Muscle FatK-means clustering in 2D • Given two images f(x,y) and g(x,y) of the same scene but representing different channels. • To segment into N regions 1. Randomly initialize N cluster centers (fk,gk) 2. For each (x,y) • Compute the distance from (f(x,y), g(x,y)) to all cluster centers (fk,gk) • Assign this pixel to cluster with the smallest distance 3. Recompute cluster centers based on pixels assigned 4. Stop if cluster centers didn’t move; otherwise, go to step 2Region growing • Connectivity can be as important as intensity in segmentation • Example: – We want to segment the ventricles in a brain MRI. – Pixels belonging to the ventricles are darker than most other pixels in the head region, but about the same intensity as the pixels in the background (air region) – What can be done?Region growing • Example: – We want to segment the ventricles in a brain MRI. – Pixels belonging to the ventricles are darker than most other pixels in the head region, but about the same intensity as the pixels in the background (air region) – Notice that air and ventricle regions are disconnected – Find a seed pixel in the ventricle region – Find the region connected to the seed pixel and also satisfying the intensity thresholdRegion growing implementation • Input intensity image f(x,y) • Let S(x,y) be a seed array containing 1s at the locations of seed points and 0s elsewhere • Let fQ(x,y) denote the result of applying a condition Q to f(x,y) such as a threshold. Q is called a predicate. fQ is 1 for all pixels passing the condition Q, 0 elsewhereRegion growing implementation 1. Find all connected components in S. For each component pick a single seed point, set other S(x,y) to 0 2. Let g(x,y) be an image formed by appending to each seed point in S all the 1-valued points in fQ that are 8-connected to that seed point. 3. Label each connected component in g(x,y) with a different region label. This is the segmented image obtained by region growing.Hierarchical segmentation • Region growing requires seeds to start from • Region merging can solve this problem – Define a region quality metric M(R) • For instance, the variance of the intensities of all pixels in the region. Small variances correspond to more homogeneous regions (higher quality) 1. Initialize all pixels as their own region 2. Compute the cost of merging any pair


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