This question will analyze your understanding and the concepts learned during classes and labs  ...

This question will analyze your understanding and the concepts learned during classes and labs  to answer this question. Describe image morphology and the operators used in morphological  operations. Describe with the help of a diagram how a morphological operations use a moving window to transform an image? Describe the equations and diagrams of common 1D and 2D windows used in morphological operations. What are the applications of morphological filters? Describe the equation and operation of dilation, erosion and open and close filters.

Image Morphology

                Morphological image processing is a collection of non-linear operations related to the shape or morphology of features in an image. Image Morphology is the set of image processing operations that perform the operations on image based on the shape. Morphological Operations change the shape of the objects in an image. These operations are binary logical operations.

A morphological operation is (conceptually) defined by moving a window over the binary image to be modified, in such a way that it is eventually centered over every image pixel, where a local logical operation is performed.

Operators used in Morphological Operations

                The morphological operators are defined in terms of simple logical operations on local groups of pixels. The logical operators that are used are the simple NOT, AND, OR, and MAJ (majority) operators. Given a binary variable x, NOT(x) is its logical complement.

Morphological operators perform a structuring element to an image taken as input and create an output image of the same size. In a morphological operation, the value of every pixel in the resultant image is based on a comparison of the corresponding pixel in the source/input image with its neighbors.

These operations are performed on two or more images. These operations follows the DeMorgan’s Laws for binary arithmetic.

How a Morphological Operations use a moving window to transform an Image

                In image morphology, binary operators are implemented through windowing or sliding window. Sliding window is a core concept in Image Processing.

Window

A window defines a geometric rule according to which gray levels are collected from the vicinity of a given pixel coordinate. It is called a window since it is often visualized as a moving collection of empty pixels that is passed over the image.

Moving/Sliding Window

                Sliding windows play an integral role in object classification, as they allow us to localize exactly “where” in an image an object resides. Utilizing both a sliding window and an image pyramid we are able to detect objects in images at various scales and locations.

Sliding windows: “slide” a box around image and classify each image crop

inside a box (contains object or not?).

Sliding window is also known as Kernel, Filter and Window. Sliding window is the matrix of size  3x3, 5x5 or 7x7. The elements of its matrix are any number.  

                                           

These are 3 different windows having same size but they have different elements.

Transformation of an Image with Moving Window

Sliding Window

 

                               

Three entities are involved in theis process that are: Original Image, Filtered Image and Kernel. The basic concept is that we have to calculate every pixel’s value in filtered image. The image size of original and filtered image is same. We have to place a Kernel in Original image on that coordinate which coordinate’s value we have to define. Then we slide that window in original image to get more values.

Equation and Diagram of Common 1D and 2D windows

Common 1D (1 Dimensional ) Window

                A 1D window is a window which have 1 row or 1 column. It means it have one row and many columns or 1 column and many rows.

Equations and Diagram of 1D

                B = ROW[2P 1] {(0,m); m P,...,P}

                B = COL[2P 1] {(n,0); n P,...,P}