Course Objectives:

To Cover the basic theory and algorithms that are widely used in digital image processing.

To Expose students to current technologies and issues that are specific to image processing systems.

To Develop hands-on experience in using computers to process images.

Familiarize with MATLAB Image Processing Toolbox.

Recommended Textbook

• “Digital Image Processing” by R.C. Gonzalez and R.E. Woods, 3rd edition, Pearson Prentice Hall, 2008

• Additional readings on the class website

Prerequisites:

Knowledge of the following three areas:

-Linear Algebra.

-Elementary Probability Theory.

-Signals and Systems.

Grading Policy

Quizzes 15%

H.W 10%

Attendance 10%

Projects 20%

FinalExam45%

Course outline

Introduction Digital Image Fundamentals Image Enhancement in the Spatial Domain Image Enhancement in the Frequency Domain Image Restoration Image Compression Image Segmentation Representation and Description

What is a Digital Image?

A finite array of data values

What is Image Processing

Processing digital images by means of a digital computer.

Image processing typically attempts to accomplish one of three things:

Restoring Images

Enhancing Images

Understanding Images

• Restoration takes a corrupted image and attempts to recreate a clean original

• Enhancement alters an image to makes its meaning clearer to human observers

• Understanding usually attempts to mimic the human visual system in extracting meaning from an image

Three Types of Processes Low-level Processes :

Involve primitive operations such as image preprocessing to reduce noise, contrast

enhancement, and image sharpening.

A low-level process is characterized by the fact that both its inputs and outputs are

images.

Mid-level Processes:

Involves tasks such as segmentation (partitioning an image into regions or objects),

description of those objects to reduce them to a form suitable for machine learning ,

and classification(recognition) of individual objects.

Its inputs generally are images, but its outputs are attributes extracted from those

images (e.g., edges, contours, and the identity of individual objects).

Three Types of Processes

High-level Processes :

Processing involves "making sense“ of an ensemble

of recognized objects, as in image analysis, and, at

the far end of the continuum, performing the

cognitive functions normally associated with vision.

Applications

Processing of remote-sensed images via satellite.

Radar, MRI, Ultrasonic image processing.

Noise Reduction.

Character recognition.

Automatic inspection of industrial parts.

Content based image retrieval.

Biometrics.

Target tracking.

Sources of Energy for Image Formation The principle energy source for images is the EM

spectrum

Other sources include ultrasonic, electronic, and synthetic images.

Some Applications -- Medical Diagnostics

Some Applications -- MRI

Imaging in Radio Band

Some Applications -- Microscopy

Some Applications -- Industrial Inspection

Some Applications -- Remote Sensing

Some Applications -- Transmitting Images

Key Stages in Digital Image Processing

Image Acquisition

Image Enhancement

Image Restoration

Morphological Processing

Segmentation

Object Recognition

Image Representation & Description

Image Compression

Colour Image Processing

Image Acquisition

Image Sampling and Quantization

Digitalization of an analog signal involves two operations: Sampling: Degitizing the x- and y-coordinates. Quantization: Degitizing the amplitude values.

Image Sampling and Quantization

Representing Ddigital Images

A digital image is composed of M rows and N columns of pixels each storing a value.

Representing Ddigital Images

A complete M × N digital image can be written in the following compact matrix form:

The right side of this equation is by definition a digital image. Each element of his matrix array is called an image element, picture element, pixel, or pel.

Storage Capacity

A digital image can be represented as a 2-D function whose coordinates and amplitude values are integers.

The digitization process requires decisions about values for M, N, and for the number, L, of discrete gray levels allowed for each pixel.

The discrete levels are equally spaced integers in the interval [0, L-1], this range is called the dynamic range of an image.

Images with high dynamic range will have high contrast and (vise versa).

The number, b, of bits required to store a digitized image is: b = M x N x k

Storage Capacity

Spatial Resolution

The spatial resolution of an image is determined by how sampling was carried out

Spatial resolution simply refers to the smallest discernable detail in an image

Vision specialists well

often talk about pixel size Graphic designers will talk

about dots per inch (dpi)

Gray-level Resolution

Gray-level resolution is the smallest discernible change in gray level.

Due to hardware considerations, the number of gray levels is usually an integer power of 2. The most common number is 8 bits, i.e 256 levels.

It is common to refer to an L-level digital image of size MxN as having a spatial resolution of MxN pixels and a gray-level resolution of L levels.

Effects of Varying Spatial Resolution

Effects of Varying Spatial Resolution

Effects of Varying Gray-Level Resolution

Ridge like structure False contouring

Effects of Varying Gray-Level Resolution

Effects of Varying Gray-Level Resolution As a very rough rule of thumb, and assuming

powers of 2 for convenience, images of size 256*256 pixels and 64 gray levels are about the smallest images that can be expected to be reasonably free of objectionable sampling checkerboards and false contouring.

Zooming Digital Images

Zooming (digital image) can be viewed by oversampling (continuous image).

1- Creation of new pixel locations

2- Assign a gray level value to this new location using:

Nearest neighbor interpolation (Pixel replication )

Bilinear interpolation

Pixel Replication

Applicable to increase the size of an image an integer number of times.

We can duplicate each column and each row. New locations are duplicates of old locations.

Fast but produces checkerboard effect that is particularly objectionable at high factor of magnification.

x4

Bilinear Interpolation

Using the four nearest neighbors of a point. Let (x’, y’) denote the coordinates of a point in

the zoomed image, the gray value v(x’,y’) will be set to:

V(x’,y’)=ax’ + by’ +cx’y’ + d Where the four coefficients are determined from

the four equations in four unknowns using the four nearest neighbors of point (x’, y’).

Image Zooming

Shrinking Digital Image

Shrinking (digital image) can be viewed by undersampling (continuous image).

1- Deletion of row column pixels.

2- Assign a gray level value using :

Nearest neighbor interpolation

Bilinear interpolation

Relationships Between Pixels

1- Neighbors of a Pixel:

The 4- neighbors of pixel p are:

N4(p)

The 4- diagonal neighbors are:

ND(p)

The 8-neighbors are :

N8(p)

P

P

P

Relationships Between Pixels

Connectivity between pixels is important Because it is used in establishing boundaries of objects and components of regions in an image

Two pixels are connected if: They are neighbors (i.e. adjacent in some sense -- e.g.

N4(p), N8(p), …) Their gray levels satisfy a specified criterion of

similarity (e.g. equality, …)

Adjacency

Let V be the set of intensity used to define djacency; e.g. V={1} in a binary image or V={100,101,102,…,120} inn a gray-scale image.

We consider three types of adjacency :

1. 4-adjacency: Two pixels p and q with values from V are 4-adjacent if

q is in the set N4(p).

2. 8-adjacency:

Two pixels p and q with values from V are 8- adjacent if q is in the set N8(p).

Adjacency

3. m-adjacency (mixed adjacency): Two pixels p and q with values from V are m- adjacent if :

(i) q is in N4(p),or

(ii) q is in ND( p)and N4( p)∩ N4(q) is empty

Two image subsets S1 and S2 are adjacent if some pixel in S1 is adjacent

to some pixel in S2.

Digital path (curve)

A (digital) path (or curve) from pixel p with coordinates (x, y)

to pixel q with coordinates (s, t) is a sequence of distinct pixels

with coordinates

(x0, y0), (x1,y1), ……., (xn, yn)

where (x0, y0) = (x, y), (xn, yn) = (s, t), and pixels (xi, yi) and (xi-1,

yi-1) are adjacent for 1≤ i ≤ n. In this case, n is the length of the

path. If (x0, y0) = (xn, yn) the path is a closed path.

Regions 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 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 S only has one connected component, then it is

called a connected set.

Let R be a subset of pixels in an image. We call R a

region of the image if R is a connected set

Region Boundary and edge

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.

An edge is a “local” concept that is based on a

measure of gray-level discontinuity at a point.

Distance Measures

Distance Measures

Distance Measures

Distance Measures

The Dm distance: the shortest m-path between the points.

Image Operations on a Pixel Basis

when we refer to an operation like “dividing one image by another,” we mean specifically that the division is carried out between corresponding pixels in the two images.

Linear and Nonlinear Operations

H is a Linear operator if:

H(af + bg) = aH(f) + bH(g)

Where a and b are two scalars and g are two images.

(i.e) the result of applying a linear operator to the sum of two images is

identical to applying the operator to the images individually, multiplying

the results by the appropriate constants, and then adding those results.

For example, an operator whose function is to compute the sum of K

images is a linear operator. An operator that computes the absolute value of

the difference of two images is not.

Reading

Sections 2.4 and 2.5 of the textbook.

Homework

Answer the following problems from the text book:

9, 11, 15,18, 19