DigitalImageFundamentalas_GM.ppt

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Digital Image Processing in Life Sciences

March 14th, 2012

Lecture number 1: Digital Image Fundamentals


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What Is Digital Image Processing?

(The Origins of Digital Image Processing)

Fundamental Steps in Digital Image Processing

Image Sampling and Quantization

Spatial and Gray-Level Resolution

Some Basic Relationships Between Pixels

Zooming and Shrinking Digital Images

Lookup tables

Color spaces

Lectures outline


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Terms to be conveyed:

Pixel

Gray level

Bit depth

Dynamic range

Connectivity types/neighborhood

Interpolation types

Look-up tables


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Book:

Digital Image Processing, Rafael C. Gonzales and Richard E.Woods

Web resources:

www.microscopy.fsu.edu (very thorough and informative)

www.cambridgeincolour.com (beautiful examples, excellent tutorials)
http://www.microscopy.fsu.edu/http://www.cambridgeincolour.com/http://www.cambridgeincolour.com/http://www.microscopy.fsu.edu/


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Next topics:

2. Image enhancement in the spatial domain

3. Segmentation

4. Image enhancement in the frequency domain

5. Multi dimensional image processing

6-7. Guest lectures-TBD


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What Is A Digital Image?

Image= a two-dimensional function, f(x,y), where x and y are spatialcoordinates, and the amplitude of f at any pair of coordinates (x, y) is

called the intensity (gray level of the image) at that point. When x, y, andthe amplitude values of f are all finite, discrete quantities, we call theimage a digital image. (Gonzalez and Woods).


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These sets of numbers can be depicted in terms of frequencies

http://cvcl.mit.edu/hybrid_gallery/gallery.html
http://cvcl.mit.edu/hybrid_gallery/gallery.htmlhttp://cvcl.mit.edu/hybrid_gallery/gallery.html


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We can define three types of computerized processes:

Low-, mid-, and high-level.

Low: image preprocessing, noise reduction, enhance contrast etc.

Mid: segmentation, sorting and classification.

High: assembly of all components into a meaningful coherent form

Digital Image Processing-Points to consider:

Why process?

Are both the input and output of a process images?

Where does image processing stop and image analysis start?

Are the processing results intended for human perception or for machine perception?

Character recognition and fingerprint comparisons vs intelligence photos


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Digital image origins-

The digital image dates back to

the 1920s and the Bartlane cable picture transmission system between NY and

London. The image took 3 hours to transmit, instead of more than one week.

They started with 5 tone levels and increased to 15 levels by 1929.

Taken from Gonzalez and Woods


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Lookup tables

Color spaces

Lectures outline


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Essential steps when processing digital images:

Acquisition

Enhancement

Restoration

Color image restoration

Wavelets

Morphological processing

Segmentation

Representation

Recognition

Outputs are

digital images

Outputs are

attributes ofthe image


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Image acquisition

Acquire or receive an image for further processing.

This step has a major impact over the entire procedure of processing and

analysis.

Image Enhancement

Improving quality subjectively (e.g. by change of contrast)

Image Restoration

Improving quality objectively (e.g. by removing psf)


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microscopy.fsu.edu


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microscopy.fsu.edu


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microscopy.fsu.edu


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Extracting components for the purpose of representing shapes

Segmentation

Deconstructing the image into its constituent objects. A crucial step for

successful recognition of the image contents.


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Extracting components for the purpose of representing shapes

Segmentation

Deconstructing the image into its constituent objects. A crucial step for

successful recognition of the image contents.

Representation

Feature selection-classification/grouping of objects


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Lookup tables

Color spaces

Lectures outline


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Keep in mind:

The sensor we used to create the image has a continuous output.

But, the transition from a continuum to a digital image requires two processes:sampling and quantization.

Sampling is the process of digitizing the spatial coordinates.

Quantization is the process of digitizing the amplitude values at those spatialcoordinates.

The arrangement of the sensor used to create the image determines the samplingmethod and its output.

Different limits determine the performance of the optical sensors and of the

mechanical sensors.

Sampling and quantization


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Sampling and quantization result in arrays of discrete quantities.

By convention, the coordinate (x,y)=(0,0) is located at the upper leftmost

corner of the image.

picture elements=image elements=pels=pixels

(Gonzales and Woods)

Sampling results in typical image sizes that can vary from 128 x 128 to 4096 x

4096 or any combination thereof.


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An Image Formation Model

Let l(x0, y0) be the gray level (gl) value at (x0, y0) : l=f (x0, y0)

l is bounded by Lmin and Lmax and the boundary [Lmin, Lmax] is the gray scale.

This interval is usually shifted to [0, L-1] where 0 represents black gl values,

and L-1 represents white gl values.


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Quantization results in discrete values of gray levels, typically an integer power of

2: L=2k .

If k=8, the result is 256 gray levels, from 0 to 255.

Dynamic range- the portion of the gray levels in the image out of the entire gray

scale of the image.

Think about high vs low dynamic range images: how does the dynamic range

affect the contrast of the image? Next lecture


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Gray level (bit-depth)

Resolution

How many bits are required to save a digital image?

b=M x N x k (or M2k for images of equal dimensions).

Size (kb)

8 (256) 12 (4096) 16 (65536)

128 16.384 24.576 32.768

256 65.536 98.304 131.072

512 262.144 393.216 524.288

1024 1048.576 1572.864 2097.152

2048 4194.304 6291.456 8388.608


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8bit images- values are integers, unsigned

16bit images- values are integers, some softwares allow signed.

32bit images-floating-point, signed.


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Lookup tables

Color spaces

Lectures outline


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Spatial and gray-level resolution

Spatial resolution is rather intuitive, and is determined by the quality and density of

the sampling.

Sampling theories (eg Nyquist-Shannon) state that sampling should be performed at

a rate that is at least twice the size of the smallest object/highest frequency.Based on this, over-sampling and under-sampling (=spatial aliasing) can occur.

Gray level resolution is a term used to describe the binning of the signal rather thanthe actual difference we managed to obtain when we quantized the signal. 8-bit and

16-bit images are the most common ones, but 10- and 12-bit images can also be

found.


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128 x 128

256 x 256

512 x 512

64 x 64

Changing the resolution of the image without changing bit-depth

checker board patterns


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2bit

3bit

4bit

8bit

1bit

Changing the bit-depth of the image without changing resolution

False contouring


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Lookup tables

Color spaces

Lectures outline


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(x+1, y), (x-1, y), (x, y+1), (x, y-1)= 4 neighbors of p, or N4(p)

(x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1, y-1)= the four diagonal neighbors, or Nd(p).

N4(p) together with Nd(p) are N8(p).

Consider the case of image borders.

Neighbors of a pixel

(x,y) (x+1, y)(x-1, y)

(x, y+1)

(x, y-1)

(x+1, y+1)

(x+1, y-1)

(x-1, y+1)

(x-1, y-1)


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Adjacency/Connectivity, Regions, and Boundaries

Pixels are said to be connected if they are neighbors and if their gray levels

satisfy a specified criterion of similarity.

Consider this example of binary

pixels

V- the set of gray levels used to define adjacency. In this binary example, V={0}

to define adjacency of pixels with the value 0. In non-binary images, the valuesof V can have a wider range.


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The region R of an image- a subset of pixels which is a connected set, meaning that

there exists a path that connects the adjacent pixels.

The boundary (=border=contour) of R is the set of pixels in R that have one or more

neighbors that are not in R.

What happens when R is the entire image?

Do not confuse boundary with edge. The edge is formed by discontinuity of gray

levels at a certain point.

In binary images, edges and boundaries correspond.


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Distances between pixels

Between (x,y) and (s,t):

Eucladian distance: given by Pythagoras

D4 distance (=city-block distance):D4(p, q) = |x s| + |y t|.

3,3

3,2

3,1

4,22,2

2,31,3 4,3 5,3

4,43,42,4

3,5

0

1

1

1

1

2 2

2

2

2

2

2

2

Diamond pattern

Pixel coordinates:


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D8(p, q) =max( |x s| , |y t|) results in a square pattern around the center pixel.

0

1

1

1

1

1 1

2

2

1

2

1

2

2 2

2

2

22

22

2

2

22


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Lookup tables

Color spaces

Lectures outline


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Zooming and shrinking digital images

Zoom: 1. Create new pixel locations

2. Assign gray level values to the locations


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For increasing the size of an image an integer number of times, the

method of pixel replication is used.

For example, when changing a 512 x 512 image to 1024 x 1024, every

column and every row in the original image is duplicated.

At high magnification factors, checkerboard patterns appear.

Nearest neighbor interpolation

Bilinear interpolation (2 x 2)

Bicubic interpolation (4 x 4)

Examples of non-adaptive interpolation

Scaling up using different methods


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Pixel replication

Bilinear

Bicubic

Scaling up using different methods


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Lookup tables

Color spaces

Lectures outline


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Look up tables:

Save computational time (LUTs can be found early in history)

Require a mapping or transformation function- an equation that converts thebrightness value of the input pixel to another value in the output pixel

Do not alter pixel values

Image transformations that involve look-up tables can be implemented by either

one of two mechanisms: at the input so that the original image data aretransformed, or at the output so that a transformed image is displayed but the

original image remains unmodified.

www.microscopy.fsu.edu
http://www.microscopy.fsu.edu/http://www.microscopy.fsu.edu/


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Lookup tables

Color spaces

Lectures outline


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There are ways to describe color images other than the RGB space

Color space=color gamut

RGB= 3 X 8-bit channels= 24bit= true color

The histograms of RGB images can be viewed either as separate channels or as

the weighted average of the channels.

Some representations of color images calculate a weighted average of green,

red and blue.

Hue-Saturation-Intensity (more intuitive as we perceive the world):


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Hue-Saturation-Intensity (more intuitive, as we perceive the world):

Hue= color spectrum, Saturation= color purity, Intensity= brightness

More: Hue-Saturation-Lightness; Hue-Saturation-Brightness


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End of Lecture 1

Thank you!

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