Chapter 2
Digital ImageFundamentals
Elements of Visual Perception
Structure of the Human Eye
Image Formation in the Eye
Brightness Adaptation and Discrimination
Light and the Electromagnetic Spectrum ()
Image Sensing and Acquisition
A Simple Image Formation Model
where
is called the illumination component
is called the reflectance component
( for a chest X-ray case, we use a transmissivity function instead of reflectivity function)
Some typical values for :
On a clear day, the sun may produce in excess of 90,000 lm/m2 of illumination on the surface of the Earth.
This figure decreases to less than 10,000 lm/m2 on a cloudy day.
On a clear evening, a full moon yields about 0.1 lm/m2 of illumination.
The typical illumination level in a commercial office is about 1000 lm/m2.
Some typical values of :
0.01 for black velvet,
0.65 for stainless steel,
0.80 for flat-white wall paint,
0.90 for silver-plated metal, and
0.93 for snow.
the gray level of the image at the point
lies in the range
The interval is called the gray scale
Image Sampling and Quantization
Basic Concepts in Sampling and Quantization
Representing Digital Images
Each element of this matrix array is called an image element, picture element, pixel, or pel.
It is advantageous to use a more traditional matrix notation to denote a digital image and its elements
A digital image can be described by a 2-D function whose coordinates and amplitude values are integers
This digitization process requires decisions about values for M,N, and for the number,L, of discrete gray levels allowed for each pixel
The number of bits required to store a digitized image is
When M=N
Spatial Resolution and Gray-Level Resolution
Aliasing and Moiré Patterns
Sampling Rate
Undersampled
Band-limited functions
Aliased frequencies
Zooming and Shrinking Digital Images
Nearest neighbor interpolation
Pixel replication
Bilinear interpolation
,
where the four coefficients are determined from the four equations in four unknowns that can be written using the four nearest neighbors of point (x', y').
Image shrinking
Expand the grid to fit over the original image, do gray-level nearest neighbor or bilinear interpolation, and then shrink the grid back to its original specified size.
Some Basic Relationships Between Pixels
Neighbors of a Pixel
A pixel p at coordinates (x, y)
has four horizontal and vertical neighbors,
four diagonal neighbors of p,
Adjacency, Connectivity, Regions, and Boundaries
Let V be the set of gray-level values used to define adjacency.
4-adjacency: Two pixels p and q with values from V are 4-adjacent if q is in the set.
8-adjacency: Two pixels p and q with values from V are 8-adjacent if q is in the set .
m-adjacency (mixed adjacency). Two pixels p and q with values from Vare m-adjacent if
q is in , or
q is in and the set has no pixels whose values are from V.
A (digital) path (or curve) from pixel p with coordinates to pixel q with coordinates is a sequence of distinct pixels with coordinates
where , and pixels and are adjacent for In this case,
n is the length of the path
connected set:
Let S represent a subset of pixels in an image. Two pixels p and q are said to be connected in S if there exists a path between them consisting entirely of pixels in S. For any pixel p in S, the set of pixels that are connected to it in S is called a connected component of S. If it only has one connected component, then set S is called a connected set.
region:
Let R be a subset of pixels in an image. We call R a region of the image if R is a connected set.
boundary :
The boundary (also called border or contour) of a region R is the set of pixels in the region that have one or more neighbors that are not in R.
Distance Measures
For pixels p,q, and z, with coordinates , , and , respectively, D is a distance function or metric if
(a) ( iff )
(b),and
(c).
Euclidean distance between p and q:
(2.5-1)
distance (also called city-block distance) between p and q:
(2.5-2)
distance (also called chessboard distance) between p and q:
(2.5-3)
Image Operations on a Pixel Basis
Linear and Nonlinear Operations