Morphology in graphics and image processing

1. 1 Overview 1 2 Introduction 2.1 The structuring element 2.2 Basic operations on sets
The basics of morphology •How to represent objects? •What are the set theoretic operations relevant to morphology? •What is a structuring element? Morphological operations •How to implement basic operations like erosion, dilation, opening, and closing? •How to choose the appropriate morphological operation for preprocessing a noisy binary image? Detecting shapes • How the Hit or Miss transform works? Morphological algorithms •How to implement a structuring element with don't care values? •How to identify region boundary and convex hull using morphological techniques? •How to obtain the skeleton of a shape? •How to do thinning and thickening of binary shapes? •How to prune off stray branches from thinned character images? Morphological reconstruction •How to remove noise or other undesirable objects in an image? •How to fill up holes in objects without any manually identifying seed points in the hole region?
MORPHOLOGY The term morphology is being used in a variety of streams like linguistics, biology, astronomy, mathematics, and it is also used with prefixes like Geo-morphology, River morphology, urban morphology, etc. The term morphology used in image processing refers to the tools which are developed using the theory developed as part of mathematical morphology.
Morphology
In its most general form, the term morphology refers to a branch of biology that deals with Form and Structure

2. of animals and plants.
Mathematical Morphology
The term has been used in mathematics where it deals with Form and Structure of regions.
Morphology in Image Processing
In image processing the term morphology deals with developing tools for extracting Form and Structure of image regions (objects). Extraction of features from in image is the first step towards image analysis. Morphology plays an important role in image processing because it can be used to develop techniques for feature extraction in binary images. Morphological tools are founded on set theoretic operations. Yet they are powerful enough to extract features of interest in an image.
Objective Of Morphology
Image components generally used for describing region shapes are:
 Boundaries
 Skeletons
 Convex Hulls
Morphological techniques are used for pre-processing and post-processing:
 to identify and enhance useful features,
 to discard (prune) noisy features.
Mathematical operations are applied to shapes/ objects. But how to represent shapes or objects in images?
Objects in Morphology
 Objects are represented as Sets.
 For binary images, each element of a set is (x;y) coordinates of white/ black pixel. These elements are (2-D integer space). Note that we don't have to explicitly code the binary value as part of the pixel representation. Since there are only 2 possible pixels (black or white) in the image, we can form a set of white pixels. All other pixels are implied to be black.
 For gray scale images such sets are i.e. 3-D integer space. The first 2 integers in the 3-tuple are the x,y coordinates and the third integer is the intensity value


3. STRUCTURED ELEMENTS.
Morphology involves the use of subimages called as structuring elements. The pixels in a structuring element can have values 0 (black), 1 (white), or may even be don't care (either black or white). The structuring element is used to assess or probe the attributes and properties of the images under study.
The origin of the structuring element is generally taken as the center of the rectangular array which contains the structuring element. However the origin need not be specified as the center. Changing the origin of the structuring element also changes the output of the morphological operations.
 We talk of morphological operations between two image objects.
 The first one is the object/ region under study.
 The second one is an object (a subimage depicting a region) used to probe the first one to identify its structural characteristics.
 All sets are padded with background elements to form a rectangular array or to provide a background border.
The structuring element is also called as a mask or a kernel.
Figure 1: Complement of a set
Basic operationoperationic operations on sets
Translation and reflection are set operations which do not involve any structuring element. Translation of a set means that each element of the set is displaced by a fixed translation distance. Reflection of a set means that the coordinate of each pixel will shift to the other side of the axis. So x becomes - x and y becomes - y.
Reflection of a set
The reflection of a set B is denoted as

4. Translation of a set
The translation of a set B by is denoted as
Set intersection
This is the traditional intersection of two sets. If the sets indicate image regions, then their intersection would give the region overlap.
Set union
This is the traditional union of two sets. If the sets indicate image regions, then their union would give the aggregate of the two regions.