Dr' Niels Lobo Computer Science

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Dr. Niels LoboComputer Science
Using the Geometric Sequence Macro in ImageJ
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Outline

• Geometric Sequence
• Using the GP Macro
• GP in ImageJ

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Geometric Sequence

• A geometric sequence (also know as geometric
  progression) is a sequence in which each term
  after the first is found by multiplying the
  pervious term by a constant, r, called the common
  ratio.
• Example 2, 6, 18, 54, ... Has the common ratio
  of 3
• An1rAn A0 scale factor r common
  ratio
• Note In your own time check Wikipedia.org and
  check that Geometric Progression and Geometric
  Sequence are the same things.

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Geometric Sequence Question

• Question What is the common ratio in this
  geometric sequence 5, 25, 125, 625, 3125
• A. 3
• B. 5
• C. 15

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Geometric Sequence

• Practical application photographer prints
  pictures.
• She charges families 10 per square inch of the
  photo paper used, because she only has limited
  supply of paper.

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Area as a Geometric Sequence

• Suppose the available sizes are 2x2,4x4,8x8,
  etc.
• Both sides increase geometrically in length
• What about the area ? 2x24, 4x416, 8x864,
  16x16256
• The area also grows geometrically ! Wow.

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Area as a Geometric Sequence

• For those of you mathematically inclined
• An1pAn Bn1qBn An1 Bn1(pq) An Bn
• The common ratio of the area is pq, where p and q
  are common ratios of the sides ! Wow.

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Area as a Geometric Sequence

• Homework
• Suppose the sizes are 2x2, 6x4, 18x8, 54x16,
• An13An Bn12Bn
• What is the common factor of An Bn ?

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Perimeter as a Geometric Sequence

• Suppose now our photographer also charges 100
  per one inch of the photo frame (she is a
  perfectionist and an expensive one to work with
  !)
• The charge is proportional to the Perimeter of
  the photo.
• Available photo sizes still form a geometric
  sequence 2x2,4x4,8x8. What about the perimeter ?

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Perimeter as a Geometric Sequence

• Sizes are 2x2, 4x4, 8x8,16x16,
• Perimeters are 2222 8, 444416, 8888
  32, 16161616 64
• Perimeter also forms geometric sequence. Wow !

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Perimeter as a Geometric Sequence

• Perimeter grows geometrically with sides. What is
  the common factor ?
• A,B sides p common factor P - perimeter
• An1pAn Bn1pBn Pn1 2(An1 Bn1)2pAn
  2pBnpPn
• The common factor of the perimeter is the same as
  the common factor of the sides. Wow !

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Using the GP Macro

• Open ImageJ
• Go to pluginsgt
• macrosgt
• run

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Using the GP Macro

• Select 111GP.txt
• This will take you to
• My Pictures, select
• any picture you like.

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Using the GP Macro

• Now, press the space bar, and notice how the
  picture increases size

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Using the GP Macro

• Notice also that the area of the picture that is
  highlighted increases as well

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Using the GP Macro

• As you keep clicking
• the space bar, it will
• eventually reach the
• end of the geometric
• sequence shown,
• and will prompt you
• for the area of the next
• number in the geometric
• sequence

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Using the GP Macro

• It is important to note that
• the cost of the paper
• increases, as the area of
• the image increases as a
• geometric sequence
• when the length and width
• of the image is multiplied
• by the constant.

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GP in ImageJ
In these equations, the new width and height of
the larger picture is calculated
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GP in ImageJ Question
In this picture What is the area equal to?