Image Processing - Representing Digital Image

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[email protected]

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1. The Electromagnetic Spectrum

2. Images are Analog

3. Sampling

4. Quantization

5. Computer Representation of Images

6. Coordinate system

7. Pixel

8. Image Classification

9. Digital Image Types

10. Megapixels

11. Digital images - bit depth

12. Sample Depth

13. How do we Use these Pixels?

14. Digital image processing and operations with matrices

16. Image Resolution

15. Resolution

17. Spatial and Gray-Level Resolution

18. Spatial Resolution by Re-sampling

19. Spatial Resolution and Pixel Count

20. Gray Level Resolution

“Virtual image, a point or system of points, on one side

of a mirror or lens, which, if it existed, would emit the

system of rays which actually exists on the other side

of the mirror or lens.”

Clerk Maxwell

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The Electromagnetic Spectrum

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Relationship between frequency ( ) and wavelength ( )

, where c is the speed of light

Energy of a photon

, where h is Planck’s constant

c

hE

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• Notice that we defined images as functions in a continuous domain.

• Images are representations of an analog world.

• Hence, as with all digital signal processing, we need to digitize our images.

Images are Analog

•Digitalization of an analog signal involves two operations:

Sampling, and

Quantization.

• Both operations correspond to a discretization of a quantity, but in different

domains.

a natural image is typically represented by a continuous or analog signal (such as a photograph, video frame, etc.)

Samples = pixels

Quantization = number of bits per pixel

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Example:

Analog Thermometer

The mercury (or alcohol) rises

continuously in direct

proportion to the temperature.

What exactly is this reading?

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Example:

Digital Thermometer

This reading is discrete.

Some detail is lost in

converting to digital

information.

What is the actual temperature?

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Sampling

Sampling corresponds to a discretization of the space. That is, of the

domain of the function, into f : [1, ...,N] [1, ...,M]

f

t

A sampled function

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Thus, the image can be seen as matrix,

The smallest element resulting from the discretization of the space is called a

pixel (picture element).

For 3-D images, this element is called a voxel (volumetric pixel).

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Quantization

Quantization corresponds to a discretization of the intensity values. That is, of

the co-domain of the function.

After sampling and quantization, we get

f

t

3

2

1

0

Quantization

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digitizing samples the natural image into discrete components

each discrete sample is averaged to represent a uniform value for that area in the image

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A picture function f(x,y) is a real-valued function of two variables, having values that are nonnegative and bounded

0 ≤ f(x,y) ≤ L-1 for all (x,y)

When a picture is digitized, a sampling process is used to extract from the picture a discrete set of samples, and then a quantization process is applied to these samples

Computer Representation of Images

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Coordinate system

We need a coordinate system to describe an image, the coordinate system

used to place elements in relation to each other is called user space, since

this is the coordinates the user uses to define elements and position them in

relation to each other.

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w An image: a multidimensional function of spatial coordinates.

w Spatial coordinate: (x,y) for 2D case such as photograph,

(x,y,z) for 3D case such as CT scan images

(x,y,t) for movies

w The function f may represent intensity (for monochrome images)

or color (for color images) or other associated values.

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PIXEL

Pixel is a smallest component of digital image

Pixel is a color point of digital image

An image should be comprised of many Pixels.

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Image classification

Bitmap image

A bitmap (or raster) image is one of the two major graphic types. Bitmap-

based images are comprised of pixels in a grid. Each pixel or "bit" in the

image contains information about the color to be displayed. Bitmap images

have a fixed resolution and cannot be resized without losing image quality

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Vector Image

Vector graphics are made up of many individual objects. Each of these objects

can be defined by mathematical statements and has individual properties

assigned to it such as color, fill, and outline. Vector graphics are resolution

independent because they can be output to the highest quality at any scale.

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Binary images: images having only two possible brightness levels (black and white).

Digital Image Types : Binary Image

Each pixel contains one bit :

1 represent white

0 represents black

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Digital Image Types : Intensity Image

Intensity image or monochrome image

each pixel corresponds to light intensity normally represented in gray scale

(gray level).

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Image Types : Index Image

Index image: Each pixel contains index number pointing to a color in a color table

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Color images: can be described mathematically as three gray scale images

Digital Image Types : RGB Image

each pixel contains a vector

representing red, green and

blue components.

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Megapixels refer to the total number of pixels in the captured image, an

easier metric is raster dimensions which represent the number of

horizontal and vertical samples in the sampling grid. An image with a

4:3 aspect ratio with dimension 2048x1536 pixels, contain a total of

2048x1535=3,145,728 pixels; approximately 3 million, thus it is a 3

megapixel image.

Megapixels

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Digital images - bit depth

The bit depth or radiometric resolution is the number of bits

used to represent each pixel

Notes Range Bits

Binary image 0-1 1

Typical grayscale image 0-255 8

High quality grayscale 0-4095 12

Very high quality grayscale 0-65535 16

Floating point format 0.0 – 1.0 32

24 bit true color (monitor) 3× 0-255 8+8+8

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Sample Depth

The values of the pixels need to

be stored in the computers

memory, this means that in the

end the data ultimately need to

end up in a binary

representation, the spatial

continuity of the image is

approximated by the spacing of

the samples in the sample grid.

The values we can represent for

each pixel is determined by the

sample format chosen.

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How do we Use these Pixels?

The image size in pixels determines what we can do with this image - how it

can be used, and if it is appropriate size for the intended use. There are two

fundamental uses which cover almost every application: printing the image on

paper (print a photo in a book, etc), or showing the image on a video screen

(snapshots or web pages, etc).

1024x768 pixels. Video screens are dimensioned in pixels, and images are

dimensioned in pixels. Inches are no factor at all on the video screen, then

for sure we don't need an image larger than that video screen size

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when we print digital images on paper, the paper is dimensioned in inches,

but digital images are dimensioned in pixels. We print the image on paper at

some printing resolution, which is specified in pixels per inch (ppi), which is

simply a spacing of pixels on paper. The image size in pixels determines the

size we can print it in inches on paper. For example, if we print 1800 pixels

width at 300 ppi, then those 1800 pixels will cover 6 inches of paper, simply

because 1800 pixels / 300 ppi = 6 inches

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Digital image processing and operations with matrices

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RESOLUTION

How quality of image

With the same size of picture

If high resolution, high memory is required to store data

If low resolution, less memory is required to store data

Its unit is call “point per inch”

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Image resolution It is an umbrella term that describes the detail an image

holds. The term applies to raster digital images, film images, and other

types of images. Higher resolution means more image details

Image Resolution

Spatial resolution: The measure of how closely lines can be resolved in an

image is called spatial resolution, and it depends on properties of the system

creating the image, not just the pixel resolution in pixels per inch (ppi). For

practical purposes the clarity of the image is decided by its spatial resolution,

not the number of pixels in an image. In effect, spatial resolution refers to the

number of independent pixel values per unit length. The spatial resolution of

computer monitors is generally 72 to 100 lines per inch, corresponding to pixel

resolutions of 72 to 100 ppi

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Spatial and Gray-Level Resolution

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Spatial Resolution by Re-sampling

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Spatial Resolution and Pixel Count

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Spatial Resolution and Pixel Size The image resolution and pixel size are often

used interchangeably. In reality, they are not equivalent. An image sampled at a

small pixel size does not necessarily has a high resolution. The following three

images illustrate this point. The first image is a SPOT image of 10 m pixel size.

It was derived by merging a SPOT panchromatic image of 10 m resolution with

a SPOT multispectral image of 20 m resolution. The effective resolution is thus

determined by the resolution of the panchromatic image, which is 10 m. This

image is further processed to degrade the resolution while maintaining the

same pixel size. The next two images are the blurred versions of the image with

larger resolution size, but still digitized at the same pixel size of 10 m. Even

though they have the same pixel size as the first image, they do not have the

same resolution

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2 4

8 16 128

32 64

256

Gray-Level Resolution

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This term refers to the size of an image, usually in reference to a photo from a

digital camera or camera phone.

Megapixel means one million pixels. The resolution of digital cameras and

camera phones is often measured in megapixels. For example, a two-

megapixel camera can produce images with two million total pixels.

Since pixels are usually square and form a grid, a 1-megapixel camera will

produce an image roughly 1200 pixels wide by 900 pixels high.

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Some well known optical illusions

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One should be able to clearly differentiate between the lines and gaps in Figure

if you can’t resolve the pattern in Figure, you might consider paying a visit to an

ophthalmologist

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