Einfhrung in Visual Computing Unit 18: Morphological Operations - PowerPoint PPT Presentation

Einführung in Visual Computing Unit 18: Morphological Operations http:// www.caa.tuwien.ac.at/cvl/teaching/sommersemester/evc  Content:  Introduction  Structuring Element  Erosion  Dilation  Opening  Closing  Hit ‐ and ‐ Miss  Thinning 1 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Introduction  Morphology denotes branch of biology that deals with form and structure of animals and plants.  Same word in the context of Mathematical Morphology : Tool for extracting image components that are useful in representation and description of region shape , such as boundaries , skeletons etc.  Language of Mathematical Morphology is set theory .  Sets in Mathematical Morphology represent objects in image.  Motive: Extract features from shape 2 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Introduction  Morph means “Shape”  We do Morphology for Shape Analysis & Shape Study.  Shape analysis easy in case of binary images , pixel locations describe the shape.  Digital Morphology is a way to describe or analyze the shape of objects in digital images 3 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Introduction  Value of each pixel in the output image is based on a comparison of the corresponding pixel in the input image with its neighbors .  By choosing size and shape of neighborhood , you can construct a morphological operation that is sensitive to specific shapes in the input image.  Morphologic operations are especially suited to the processing of binary and greyscale images.  Good for, e.g.,  Noise removal in background  Removal of holes in foreground / background 4 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Basic Concepts From Set Theory Let A and B be sets.  To indicate a is an element of A write a A.  To indicate a is not an element of A write a A.    A is a subset of B, written A B, if for every a A, a B .      The union of A and B, A B x | x A or x B .       The intersecti on of A and B, A B x | x A and x B .      c The complement of A, A x | x A .       The difference of A and B, A B x | x A and x B . 5 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Examples A  B A  B A A A B B B c A   c A B A B  A A B 6 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Dilation and Erosion  Dilation and Erosion are the two fundamental morphological operations .  Dilation adds pixels to the boundaries of objects in an image, while erosion removes pixels on object boundaries .  In morphological dilation and erosion operations, the state of any given pixel in the output image is determined by applying a rule to the corresponding pixel and its neighbors in the input image .  The rule used to process the pixels defines the operation as Dilation or Erosion . 7 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

A first Example: Erosion  Erosion is an important morphological operation  Applied Structuring Element: 8 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Example for Erosion 1 0 0 0 1 1 1 0 1 1 Input image 1 1 1 Structuring Element 0 Output Image 9 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Example for Erosion 1 0 0 0 1 1 1 0 1 1 Input image 1 1 1 Structuring Element 0 0 Output Image 10 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Example for Erosion 1 0 0 0 1 1 1 0 1 1 Input image 1 1 1 Structuring Element 0 0 0 Output Image 11 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Example for Erosion 1 0 0 0 1 1 1 0 1 1 Input image 1 1 1 Structuring Element 0 0 0 0 Output Image 12 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Example for Erosion 1 0 0 0 1 1 1 0 1 1 Input image 1 1 1 Structuring Element 0 0 0 0 1 Output Image 13 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Example for Erosion 1 0 0 0 1 1 1 0 1 1 Input image 1 1 1 Structuring Element 0 0 0 0 1 0 Output Image 14 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Example for Erosion 1 0 0 0 1 1 1 0 1 1 Input image 1 1 1 Structuring Element 0 0 0 0 1 0 0 Output Image 15 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Example for Erosion 1 0 0 0 1 1 1 0 1 1 Input image 1 1 1 Structuring Element 0 0 0 0 1 0 0 0 Output Image 16 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Dilation & Erosion  Basic operations  Are dual to each other:  Erosion shrinks foreground, enlarges Background  Dilation enlarges foreground, shrinks background 17 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Structuring Element

Structuring Element  Essential part of morphological operations is the Structuring Element used to probe the input image.  Two ‐ dimensional structuring elements consist of a matrix of 0’s and 1’s, much smaller than the image being processed.  Structuring Elements can have varying sizes  Element values are 0,1 and none (!)  Structural Elements have origin (anchor pixel) 19 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Structuring Elements  The center pixel of the structuring element, called the origin , identifies the pixel of interest—the pixel being processed.  The pixels in the structuring element containing 1’s define the neighborhood of the structuring element. 20 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Example of Structuring Elements (Kernels)  Empty spots in the Structuring Elements are don’t care’s! Box Disc 21 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Erosion

Erosion  Erosion is the set of all points in the image, where the structuring element “ fits into ”.  Consider each foreground pixel in the input image  If the structuring element fits in, write a “1” at the origin of the structuring element!  Simple application of pattern matching  Input:  Binary Image (Gray value)  Structuring Element, containing only 1s! 23 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Erosion  Brief Description  To delete or to reduce something  Pixels matching a given pattern are deleted from the image.  Basic effect Erode away the boundaries of regions of foreground pixels (i.e. white pixels, typically). Common names: Erode, Shrink, Reduce 24 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Erosion  How It Works A   A & B are sets in Z², the erosion of A by B, denoted as B     z  ( ) A B z B A  In words, this equation indicates that the erosion of A by B is the set of all points z such that B , translated by z , is contained in A . 25 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Erosion Effect of erosion using a 3 × 3 square structuring element Set of coordinate points = { ( ‐ 1, ‐ 1), (0, ‐ 1), (1, ‐ 1), ( ‐ 1, 0), (0, 0), (1, 0), ( ‐ 1, 1), (0, 1), (1, 1) } A 3 × 3 square structuring element 26 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Erosion  Erosion By a Rectangular Structuring Element B A A  B 27 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Another Example of Erosion  White = 0, black = 1, dual property, image as a result of erosion gets darker 28 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Matlab Programming: Erosion %Read image I = imread(‘ford.tiff'); figure('Name', 'original'); imshow(I); %create structuring elements % 11 ‐ by ‐ 11 square se1 = strel('square',11); %Apply erosion operation figure('Name', 'Erode'); Ierode1 = imerode(I,se1); %Show the result image subplot(1,1,1), imshow(Ierode1), title('11x11 square'); 29 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Iterative Operation of Erosion Original Image after 1 erosion after 5 erosions after inf erosions 30 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Counting Coins  Counting coins is difficult because they touch each other!  Solution: Binarization and Erosion separates them! 31 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations

Dilation

Dilation  Dilation is the set of all points in the image, where the structuring element “ touches ” the foreground .  Consider each pixel in the input image  If the structuring element touches the foreground image, write a “1” at the origin of the structuring element!  Input:  Binary Image  Structuring Element, containing only 1s!! 33 Robert Sablatnig, Computer Vision Lab, EVC ‐ 18: Morphological Operations