Lecture 3 Digital Image Processing Aliasing Can aliasing

Lecture 3 Digital Image Processing

Aliasing • Can aliasing be avoided in images? • NO! – Images are practically of a finite spatial duration => Not bandlimited! => Aliasing always occurs http: //ptolemy. eecs. berkeley. edu/eecs 20/week 13/moire. html

Basic terminology • Neighborhood of a pixel: (x, y)

Basic terminology • Adjacency – Two pixels are considered adjacent if they are spatial neighbors and have grey-level values from a set V. • Let – 4 -adjacency: p & q are 4 -adjacent if – 8 -adjacency: p & q are 8 -adjacent if – m-adjacency: p & q are m-adjacent if or 0 1 1 0 0 0 1 V = {1}

Digital path • A digital path is a sequence of distinct pixels with consecutive pixels being adjacent with respect to a chosen adjacency criteria. 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 • Closed paths are also allowed. • Length of the path = Number of links.

Connectedness • Two pixels are said to be connected in a subset S of pixels, if there exists a path between them that entirely lies in S. • Subset of pixels in S that are connected to each other in S is called the connected component. • Connectedness is an equivalence relation

Connectedness • A subset of pixels forming a connected set is also called a region. • Boundary of a region is the set of pixels in the region whose neighborhood contains atleast 1 pixel which is not in the region.

Application Count the number of components in the image

Application Convert into a binary image

Application

Application 11 components !

Neighborhoods • Neighborhoods can be generalized based on distance measures on a plane. – Neighborhood: • What distance(metric)? – Any function that satisfies

Neighborhood • 2 points – – Euclidean distance – City block distance – Chessboard distance – m-distance = length of the m-path between the pixels. • Also depends on the grey-level value set V