image processing - representing digital image
DESCRIPTION
TRANSCRIPT
October 7, 2013 1
October 7, 2013 2
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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