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Binary Image Analysis Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr

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CS 484, Spring 2007©2007, Selim Aksoy2 Outline Introduction to binary image analysis Mathematical morphology Pixels and neighborhoods Connected components analysis Automatic thresholding

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CS 484, Spring 2007©2007, Selim Aksoy3 Binary image analysis Binary image analysis consists of a set of operations that are used to produce or process binary images, usually images of 0s and 1s where 0 represents the background, 1 represents the foreground. 00010010001000 00011110001000 00010010001000

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CS 484, Spring 2007©2007, Selim Aksoy4 Application areas Document analysis Industrial inspection Medical imaging Adapted from Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy5 Operations Separate objects from background and from one another. Aggregate pixels for each object. Compute features for each object.

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CS 484, Spring 2007©2007, Selim Aksoy6 Example: red blood cell image Many blood cells are separate objects. Many touch each other bad! Salt and pepper noise is present. How useful is this data? 63 separate objects are detected. Single cells have area of about 50 pixels. Adapted from Linda Shapiro, U of Washington

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CS 484, Spring 2007©2007, Selim Aksoy7 Thresholding Binary images can be obtained from gray level images by thresholding. Assumptions for thresholding: Object region of interest has intensity distribution different from background. Object pixels likely to be identified by intensity alone: intensity > a intensity < b a < intensity < b Works OK with flat-shaded scenes or engineered scenes. Does not work well with natural scenes.

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CS 484, Spring 2007©2007, Selim Aksoy8 Use of histograms for thresholding Background is black. Healthy cherry is bright. Bruise is medium dark. Histogram shows two cherry regions (black background has been removed). Adapted from Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy9 Mathematical morphology The word morphology refers to form and structure. In computer vision, it is used to refer to the shape of a region. The language of mathematical morphology is set theory where sets represent objects in an image. We will discuss morphological operations on binary images whose components are sets in the 2D integer space Z 2.

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CS 484, Spring 2007©2007, Selim Aksoy10 Mathematical morphology Mathematical morphology consists of two basic operations dilation erosion and several composite relations opening closing conditional dilation …

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CS 484, Spring 2007©2007, Selim Aksoy11 Dilation Dilation expands the connected sets of 1s of a binary image. It can be used for growing features filling holes and gaps Adapted from Linda Shapiro, U of Washington

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CS 484, Spring 2007©2007, Selim Aksoy12 Erosion Erosion shrinks the connected sets of 1s of a binary image. It can be used for shrinking features removing bridges, branches and small protrusions Adapted from Linda Shapiro, U of Washington

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CS 484, Spring 2007©2007, Selim Aksoy13 Basic concepts from set theory

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CS 484, Spring 2007©2007, Selim Aksoy14 Basic concepts from set theory Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy15 Basic concepts from set theory

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CS 484, Spring 2007©2007, Selim Aksoy16 Logic operations Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy17 Structuring elements Structuring elements are small binary images used as shape masks in basic morphological operations. They can be any shape and size that is digitally representable. One pixel of the structuring element is denoted as its origin. Origin is often the central pixel of a symmetric structuring element but may in principle be any chosen pixel.

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CS 484, Spring 2007©2007, Selim Aksoy18 Structuring elements Adapted from Gonzales and Woods, and Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy19 Dilation

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CS 484, Spring 2007©2007, Selim Aksoy20 Dilation Binary image A Structuring element B Dilation result 1111111 1111 1111 11111 1111 11 111 111 111 11111111 11111111 11111111 01111111 01111111 01111111 01111111 01111000 (1 st definition)

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CS 484, Spring 2007©2007, Selim Aksoy21 Dilation Structuring element B Dilation result 1111111 1111 1111 11111 1111 11 111 111 111 11111111 11111111 11111111 1111111 1111111 1111111 1111111 1111 (2 nd definition) Binary image A

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CS 484, Spring 2007©2007, Selim Aksoy22 Dilation Pablo Picasso, Pass with the Cape, 1960 Structuring Element Adapted from John Goutsias, Johns Hopkins Univ.

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CS 484, Spring 2007©2007, Selim Aksoy23 Dilation Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy24 Erosion

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CS 484, Spring 2007©2007, Selim Aksoy25 Erosion Binary image A Structuring element B Erosion result 1111111 1111 1111 11111 1111 11 111 111 111 00000000 00000000 00001100 00001100 00001100 00000000 00000000 00000000 (1 st definition)

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CS 484, Spring 2007©2007, Selim Aksoy26 Erosion Structuring element B Erosion result 1111111 1111 1111 11111 1111 11 111 111 111 11 11 11 (2 nd definition) Binary image A

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CS 484, Spring 2007©2007, Selim Aksoy27 Erosion Pablo Picasso, Pass with the Cape, 1960 Structuring Element Adapted from John Goutsias, Johns Hopkins Univ.

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CS 484, Spring 2007©2007, Selim Aksoy28 Erosion Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy29 Opening

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CS 484, Spring 2007©2007, Selim Aksoy30 Opening Structuring element B Opening result 1111111 1111 1111 11111 1111 11 111 111 111 11 11 11 1111 11 11 11 1111 Binary image A

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CS 484, Spring 2007©2007, Selim Aksoy31 Opening Pablo Picasso, Pass with the Cape, 1960 Structuring Element Adapted from John Goutsias, Johns Hopkins Univ.

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CS 484, Spring 2007©2007, Selim Aksoy32 Closing

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CS 484, Spring 2007©2007, Selim Aksoy33 Closing Binary image A Structuring element B Closing result 1111111 1111 1111 11111 1111 11 111 111 111 111111 11111 11111 11111 11111 11

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CS 484, Spring 2007©2007, Selim Aksoy34 Examples Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy35 Examples Original imageEroded onceEroded twice

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CS 484, Spring 2007©2007, Selim Aksoy36 Examples Original image Opened twice Closed once

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CS 484, Spring 2007©2007, Selim Aksoy37 Examples Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy38 Examples Gear tooth inspection <- original binary image <- detected defects How did they do it? Adapted from Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy39 Examples Adapted from Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy40 Properties

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CS 484, Spring 2007©2007, Selim Aksoy41 Properties

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CS 484, Spring 2007©2007, Selim Aksoy42 Boundary extraction

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CS 484, Spring 2007©2007, Selim Aksoy43 Boundary extraction Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy44 Conditional dilation

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CS 484, Spring 2007©2007, Selim Aksoy45 Region filling

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CS 484, Spring 2007©2007, Selim Aksoy46 Region filling Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy47 Region filling Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy48 Hit-or-miss transform

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CS 484, Spring 2007©2007, Selim Aksoy49 Hit-or-miss transform Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy50 Thinning

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CS 484, Spring 2007©2007, Selim Aksoy51 Thinning

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CS 484, Spring 2007©2007, Selim Aksoy52 Thickening

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CS 484, Spring 2007©2007, Selim Aksoy53 Thickening Adapted from Gonzales and Woods

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CS 484, Spring 2007©2007, Selim Aksoy54 Examples Detecting runways in satellite airport imagery http://www.mmorph.com/mxmorph/html/mmdemos/mmdairport.html

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CS 484, Spring 2007©2007, Selim Aksoy55 Examples Segmenting letters, words and paragraphs http://www.mmorph.com/mxmorph/html/mmdemos/mmdlabeltext.html

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CS 484, Spring 2007©2007, Selim Aksoy56 Examples Extracting the lateral ventricle from an MRI image of the brain http://www.mmorph.com/mxmorph/html/mmdemos/mmdbrain.html

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CS 484, Spring 2007©2007, Selim Aksoy57 Examples Detecting defects in a microelectronic circuit http://www.mmorph.com/mxmorph/html/mmdemos/mmdlith.html

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CS 484, Spring 2007©2007, Selim Aksoy58 Examples Decomposing a printed circuit board in its main parts http://www.mmorph.com/mxmorph/html/mmdemos/mmdpcb.html

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CS 484, Spring 2007©2007, Selim Aksoy59 Examples Grading potato quality by shape and skin spots http://www.mmorph.com/mxmorph/html/mmdemos/mmdpotatoes.html

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CS 484, Spring 2007©2007, Selim Aksoy60 Examples Classifying two dimensional pieces http://www.mmorph.com/mxmorph/html/mmdemos/mmdpieces.html

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CS 484, Spring 2007©2007, Selim Aksoy61 Pixels and neighborhoods In many algorithms, not only the value of a particular pixel, but also the values of its neighbors are used when processing that pixel. The two most common definitions for neighbors are the 4-neighbors and the 8-neighbors of a pixel.

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CS 484, Spring 2007©2007, Selim Aksoy62 Pixels and neighborhoods

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CS 484, Spring 2007©2007, Selim Aksoy63 Pixels and neighborhoods

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CS 484, Spring 2007©2007, Selim Aksoy64 Connected components analysis Suppose that B is a binary image and that B[r,c] = B[r,c] = v where either v = 0 or v = 1. The pixel [r,c] is connected to the pixel [r,c] with respect to value v if a sequence of pixels forms a connected path from [r,c] to [r,c] in which all pixels have the same value v, and each pixel in the sequence is a neighbor of the previous pixel in the sequence. A connected component of value v is a set of pixels, each having value v, and such that every pair of pixels in the set are connected with respect to v.

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CS 484, Spring 2007©2007, Selim Aksoy65 Connected components analysis Once you have a binary image, you can identify and then analyze each connected set of pixels. The connected components operation takes in a binary image and produces a labeled image in which each pixel has the integer label of either the background (0) or a component. Binary image after morphologyConnected components

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CS 484, Spring 2007©2007, Selim Aksoy66 Connected components analysis Methods for connected components analysis: Recursive tracking (almost never used) Parallel growing (needs parallel hardware) Row-by-row (most common) Classical algorithm Run-length algorithm (see Shapiro-Stockman) Adapted from Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy67 Connected components analysis Recursive labeling algorithm: 1. Negate the binary image so that all 1s become -1s. 2. Find a pixel whose value is -1, assign it a new label, call procedure search to find its neighbors that have values -1, and recursively repeat the process for these neighbors.

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CS 484, Spring 2007©2007, Selim Aksoy68 Adapted from Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy69 Connected components analysis Row-by-row labeling algorithm: 1. The first pass propagates a pixels label to its neighbors to the right and below it. (Whenever two different labels can propagate to the same pixel, these labels are recorded as an equivalence class.) 2. The second pass performs a translation, assigning to each pixel the label of its equivalence class. A union-find data structure is used for efficient construction and manipulation of equivalence classes represented by tree structures.

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CS 484, Spring 2007©2007, Selim Aksoy70 Connected components analysis Adapted from Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy71 Connected components analysis Adapted from Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy72 Connected components analysis Adapted from Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy73

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CS 484, Spring 2007©2007, Selim Aksoy74 Automatic thresholding How can we use a histogram to separate an image into 2 (or several) different regions? Is there a single clear threshold? 2? 3? Adapted from Shapiro and Stockman

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CS 484, Spring 2007©2007, Selim Aksoy75 Automatic thresholding: Otsus method Assumption: the histogram is bimodal. Method: find the threshold t that minimizes the weighted sum of within-group variances for the two groups that result from separating the gray levels at value t. The best threshold t can be determined by a simple sequential search through all possible values of t. If the gray levels are strongly dependent on the location within the image, local or dynamic thresholds can also be used. t Group 1 Group 2

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CS 484, Spring 2007©2007, Selim Aksoy76 Automatic thresholding: Otsus method Adapted from Shapiro and Stockman

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