MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C7FD2C.D286B3A0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C7FD2C.D286B3A0 Content-Location: file:///C:/D9022913/01BinaryImages.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Binary Image Algorithm

This presentation contains content that your browser may not be able to = show properly. This presentation was optimized for more recent versions of Micro= soft Internet Explorer.

If you would like to proceed anyway, click here.

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Click to edit Ma= ster title style
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‹date/time› =
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‹date/time&= #8250;
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------=_NextPart_01C7FD2C.D286B3A0 Content-Location: file:///C:/D9022913/01BinaryImages_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C7FD2C.D286B3A0 Content-Location: file:///C:/D9022913/01BinaryImages_files/editdata.mso Content-Transfer-Encoding: base64 Content-Type: application/x-mso QWN0aXZlTWltZQAAAfAEAAAA/////0AAA/AJAAAAAAAlBAEAAAABAAAL8AQAAAASNFZ4 ------=_NextPart_01C7FD2C.D286B3A0 Content-Location: file:///C:/D9022913/01BinaryImages_files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Binary Image Algorithm
Binary Image Algorithm
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What is = an Object?
•What is an object?
–Binary image = ;
•Connected cluste= r of black pixels on a white background
•Connected cluste= r of white pixels on a black background
•Objects can also= have holes in them
2
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Content-Type: image/gif R0lGODlhGQAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAX AA4AgAAAAAAAAAIURI6pC7YPo5y02ouz3rz76nChBhQAOx== ------=_NextPart_01C7FD2C.D286B3A0 Content-Location: file:///C:/D9022913/01BinaryImages_files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Binary Image Algorithm
Goals of Image Analysis
&#= 8226;Identify objects
&= #8211;Objects can have holes in them
&#= 8226;Find their locations
&#= 8226;Find their size
• <= /div>
= 226;If certain objects are small, it can be ignored.
= 226;The decision to ignore any size object is taken by the user<= /div>
------=_NextPart_01C7FD2C.D286B3A0 Content-Location: file:///C:/D9022913/01BinaryImages_files/slide0016.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Binary Image Algorithm
Loss less Processing
•Noth= ing is removed or ignored
•No iteration, approximation
•No floating point arithmetic
4
Cell Decomposition
•Object is repres= ented by
–List of pair of numbers
•Pixel is square&= #13;
–Instead of a poi= nt
5
Definitions
•Definitions =
–A vertex is a 0-cell
–An edge is a 1-cell
•Boundaries consi= sts of 2 end-points as 0-cells
•
•
•
–A pixel is a 2-cell
•Boundaries consi= sts of 4 edges as 1-cell
•
•
–A voxel is a 3-cell
•Boundaries consi= sts of 6 faces as 2-cells
•
3D"pixel 3Dvoxel
6
Cell Decomposition of an Image
Two adjacent edges as 1-ce= lls
share a vertex, a 0-cell
Two adjacent pixels as 2-ce= lls
share an edge, 1-cell
Edge: 1-cell
Edge: 1-cell
Vertex: 0-cell
<= ![endif]>
Edge: 1-cell
The image is made of k-cells that are attached to each other along (k-1) cells= .
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Binary Images
ASSUMPTION:
Binary images are analyzed= as if they have
black objects on
white background
Background
Objects
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Cycles
•0= -cycles represent objects or connected components of the image <= /div>
–T= raversed clockwise
•1= -cycles represents holes
–T= raversed counterclockwise
3D"Binary_image" 3DCycles
Image<= /div>
Its topological features are represented as cycles= . Here A and B are 0-cycles,
C and C’ are 1-cycles= .
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/GH/AENeuf8Agxm/+Ko/4Tvxh/0Neuf+DGb/AOKo/wCE78Yf9DXrn/gxm/8AiqP+E78Yf9DXrn/g xm/+Ko/4Tvxh/wBDXrn/AIMZv/iqP+E78Yf9DXrn/gxm/wDiqP8AhO/GH/Q165/4MZv/AIqj/hO/ GH/Q165/4MZv/iqP+E78Yf8AQ165/wCDGb/4qsi91C81O8ku7+7nu7qTG+a4kMjtgADLHJOAAPwr /9k= ------=_NextPart_01C7FD2C.D286B3A0 Content-Location: file:///C:/D9022913/01BinaryImages_files/slide0022.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Binary Image Algorithm
Partition
= 226;A partition is a collection of non-overlapping regions
&= #8211;Connected set of black pixels
&= #8211;Connected set of white pixels
= 226;The partition is achieved by finding boundaries of these regions= as 0-cycles and 1-cycles.
------=_NextPart_01C7FD2C.D286B3A0 Content-Location: file:///C:/D9022913/01BinaryImages_files/slide0023.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Binary Image Algorithm
Algorithm to Detect Cycles
<= span class=3DBB style=3D'position:absolute;left:-4.43%'>•Increment= al
<= span class=3DBB style=3D'position:absolute;left:-3.71%'>•One pixel= at a time are added to the image
•The proce= ss of adding a pixel starts with adding its vertices and then its edg= es
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The Pro= cedure to Add a Pixel
3D"Steps
Stage 1-4
3D"Step 3D"Step 3D"Step
Stage 5
Stage 7
Stage 8
3D"Step
Stage 6
3D"Step
Stage 9
3D"Graph_cycles_2"
Add 4 vertex
Add 4 Edges
Add Pi= xel
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Content-Type: text/html; charset="us-ascii" Binary Image Algorithm
Example 1
3D"8_pixels_cycles"
This object has
one 0-cycle “A”=
one 1-cycle “B”=
<= /div>
3D"8_pixels_graph.jpg"
Incremental addition of pixels will able to recognize the 2 cycles
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Example 1: Add Pixel 1 and 2
Add Pixel 1
Add 4 vertex
Add 4 edges
Add 1 cycle
9 Steps
<= ![endif]> = <= ![endif]> = 3D"8_pixels_cycles"
1
Add Pixel 2
Add 2 vertex
Add 3 edges
Add 1 cycle
6 Steps
= = <= ![endif]>
1
= =
2
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Content-Location: file:///C:/D9022913/01BinaryImages_files/slide0032.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Binary Image Algorithm
Example 1: Add Pixel 3 and 4
3D"8_pixels_cycles"
Add Pixel 3
Add 2 vertex
Add 3 edges
Add 1 cycle
6 Steps