Filters (Spatial): Unsharp Mask and Filters (Spatial) Laplacian: Difference between pages

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When applied to an image, this algorithm produces a sharpened version of the image or the image volume defined by [[Delineating volumes of interest (VOIs)|a VOI of the image]].  
''Edge detection'' is the identification of meaningful discontinuities in gray level or color images. Edges are formed between two regions that have differing intensity values. This algorithm calculates the laplacian of an image (or VOI of the image) using the second derivatives (''Gxx'', ''Gyy'', and ''Gzz'' [3D]) of the Gaussian function at a user-defined scale sigma [standard deviation (SD)] and convolving it with image. The convolution of the second derivatives of the Gaussian with an image is a robust method of extracting edge information. By varying the SD, a scale-space of edges can easily be constructed.


The sharpening process works by utilizing a low-pass filtered (blurred) version of the original image. This is then subtracted away from the original to detect the presence of edges, creating the unsharp mask (effectively a high-pass filter). Contrast is then selectively increased along these edges using this mask — leaving behind a sharper final image.
=== Background ===


The effect of a high-pass filter, like the unsharp mask technique, is to enhance sharp intensity transitions (i.e., edges) but at the cost of enhancing noise.
Figure 1 shows the 1D signal of an object. The first derivative of the object is shown next. Last, the Laplacian (defined later) is shown. Note that the zero-crossing of the second derivative corresponds to the edges of the object.


== Image types ==
<div>
 
{| border="1" cellpadding="5"
|+ <div>'''Figure 1. Edge detection using laplacian operators''' </div>
|-
|
<div><div align="left">[[Image:LaplacianGrid5.jpg]]</div> </div>
|}
 
</div>
 
The laplacian function is defined as:''''
 
<math>
\triangledown^2G(x,y) = \frac {\partial^2G}{\partial x^2} + \frac {\partial^2G}{\partial y^2}
</math>
 
An efficient method of calculating the laplacian is to analytically calculate the second derivatives of Gaussian and convolve the sum with the image. The equation for this calculation follows:
 
<div align="left">[[Image:FiltersSpatialLaplacian5.jpg]]</div> <div>
 
{| border="1" cellpadding="5"
|+ <div>'''Figure 2. (A) Original MR image; (B) laplacian results; and (C) extraction of the zero crossing of the laplacian (object edges)''' </div>
|-
|
<div><div><center>[[Image:exampleLaplacianProcessing.jpg]]</center></div> </div>
|}
 
</div><div><br /> </div>
 
==== Image types ====


You can apply this algorithm to all image data types, except complex and RGB images, and to 2D, 2.5D, 3D, and 4D images.
You can apply this algorithm to all image data types except complex and to 2D, 2.5D, and 3D images.


== Applying the algorithm ==
==== Special notes ====
 
The resulting image is, by default, a float type image.
 
To achieve 2.5D blurring (each slice of the volume is processed independently) of a 3D dataset, select Process each slice independently (2.5D) in the Laplacian dialog box (Figure 3).
 
==== References ====
 
Refer to the following references for more information about this algorithm:
 
Tony Lindeberg, "Linear Scale-Space I: Basic Theory," ''Geometry-Driven Diffusion in Computer Vision'', Bart M. Ter Har Romeney, ed. (Dordrecht, The Netherlands: Kluwer Academic Publishers, 1994), pp. 1-38.
 
J. J. Koenderink, "The Structure of Images," ''Biol Cybern'' 50:363-370, 1984.
 
Raphael C. Gonzalez and Richard E. Woods, ''Digital Image Processing'' (Boston: Addison-Wesley, 1992).
 
=== Applying the Laplacian algorithm ===


To run this algorithm, complete the following steps:
To run this algorithm, complete the following steps:


# Select Algorithms &gt; Filter (spatial) &gt; Unsharp mask. The Unsharp Mask dialog box (Figure 1) opens.
# Select Algorithms &gt; Filter &gt; Laplacian. The Laplacian dialog box opens (Figure 3).
# Complete the information in the dialog box.
# Complete the fields in the dialog box.
# Click OK.
# When complete, click OK. The algorithm begins to run.


; The algorithm begins to run, and a pop-up window appears with the status. The following message appears: "Unsharp Masking Image."
; A pop-up window appears with the status. The following message appears: "Calculating the Laplacian."
; When the algorithm finishes running, the pop-up window closes, and the results either appear in a new window or replace the image to which the algorithm was applied.
; When the algorithm finishes, the pop-up window closes. Depending on whether you selected New Image or Replace Image, the results either appear in a new window or replace the image to which the algorithm was applied.


<div>
<div>.


{| border="1" cellpadding="5"
{| border="1" cellpadding="5"
|+ <div>'''Figure 1. Unsharp Mask dialog box''' </div>
|+ <div>'''Figure 3. Laplacian dialog box ''' </div>
|-
|-
|
|
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<div>Specifies the standard deviation (SD) of Gaussian in the ''X'' direction. </div>
<div>Specifies the standard deviation (SD) of Gaussian in the ''X'' direction. </div>
| rowspan="6" colspan="1" |
| rowspan="6" colspan="1" |
<div><div align="left">[[Image:dialogboxUnsharpMask.jpg]]</div> </div><div> </div>
<div><div><center>[[Image:dialogboxLaplacian.jpg]]</center></div> </div><div><br /> </div><div><br /> </div>
|-
|-
|
|
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|
|
<div>Specifies the SD of Gaussian in the ''Z'' direction. </div>
<div>Specifies the SD of Gaussian in the ''Z'' direction. </div>
|-
|
<div>'''Amplification factor''' </div>
|
<div>Applies, by default, the classical laplacian factor of 1.0; values greater than 1.0 and less than 1.2 enable the laplacian to act as a high-pass, or high-boost, filter. </div>
|-
|-
|
|
<div>'''Use image resolutions to normalize Z scale''' </div>
<div>'''Use image resolutions to normalize Z scale''' </div>
|
|
<div>Normalizes the Gaussian to compensate for the difference if the voxel resolution is less between slides than the voxel resolution in-plaine. This option is selected by default. </div>
<div>Normalizes the Gaussian to compensate for the difference if the voxel resolution is less than the voxel resolution inplane. </div>
|-
|-
|
|
<div>'''Process each slice independently (2.5D)''' </div>
<div>'''Process each edge independently (2.5D)''' </div>
|
|
<div>Filters each slice of the dataset independently of adjacent slices. </div>
<div>Blurs each slice of the dataset independently. </div>
|-
|-
|
|
<div>'''Image - (k&lt;1) * blurred image''' </div>
<div>'''Output edge image''' </div>
| rowspan="1" colspan="2" |
<div>Produces a binary image that represents the edges defined by the 0 crossings of the laplacian </div>
|-
|
|
<div>Determines the amount of filtering, or sharpening, applied to the edges of the image or a VOI of the image. Low values sharpen image edges but increase noise. The default value is 0.75. </div>
<div>'''Threshold edge noise between &lt;_&gt; and &lt;_&gt;''' </div>
| rowspan="1" colspan="2" |
<div>Limits the threshold edge noise to the range that you specify between the 0 crossings of the laplacian; the default range is -10 to 10. </div>
|-
|-
|
|
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<div>'''OK''' </div>
<div>'''OK''' </div>
| rowspan="1" colspan="2" |
| rowspan="1" colspan="2" |
<div>Applies the algorithm according to the specifications in this dialog box.  </div>
<div>Applies the laplacian algorithm according to the specifications in this dialog box.  </div>
|-
|-
|
|
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== See also: ==
== See also: ==
**[[Fast Fourier Transformation (FFT)]]
**[[Filters (Spatial): Adaptive Noise Reduction]]
**[[Filters (Spatial): Adaptive Noise Reduction]]
**[[Filters (Frequency)]]
**[[Filters (Frequency)]]
Line 107: Line 165:
**[[Filters (Spatial): Median]]
**[[Filters (Spatial): Median]]
**[[Filters (Spatial): Mode]]
**[[Filters (Spatial): Mode]]
**[[Filters (Spatial): Nonlinear Noise Reduction]]
**[[Filters (Spatial): Nonmaximum Suppression]]
**[[Filters (Spatial): Nonmaximum Suppression]]
**[[Filters (Spatial): Nonlinear Noise Reduction|Nonlinear Noise Reduction]]
**[[Filters (Spatial): Regularized Isotropic (Nonlinear) Diffusion]]
**[[Filters (Spatial): Regularized Isotropic (Nonlinear) Diffusion]]
**[[Filters (Spatial): Slice Averaging]]
**[[Filters (Spatial): Slice Averaging]]
**[[Filters (Spatial): Unsharp Mask]]


[[Category:Help]]
[[Category:Help]]
[[Category:Help:Algorithms]]
[[Category:Help:Algorithms]]

Latest revision as of 16:28, 9 February 2024

Edge detection is the identification of meaningful discontinuities in gray level or color images. Edges are formed between two regions that have differing intensity values. This algorithm calculates the laplacian of an image (or VOI of the image) using the second derivatives (Gxx, Gyy, and Gzz [3D]) of the Gaussian function at a user-defined scale sigma [standard deviation (SD)] and convolving it with image. The convolution of the second derivatives of the Gaussian with an image is a robust method of extracting edge information. By varying the SD, a scale-space of edges can easily be constructed.

Background

Figure 1 shows the 1D signal of an object. The first derivative of the object is shown next. Last, the Laplacian (defined later) is shown. Note that the zero-crossing of the second derivative corresponds to the edges of the object.

Figure 1. Edge detection using laplacian operators
LaplacianGrid5.jpg

The laplacian function is defined as:'

An efficient method of calculating the laplacian is to analytically calculate the second derivatives of Gaussian and convolve the sum with the image. The equation for this calculation follows:

FiltersSpatialLaplacian5.jpg
Figure 2. (A) Original MR image; (B) laplacian results; and (C) extraction of the zero crossing of the laplacian (object edges)
ExampleLaplacianProcessing.jpg

Image types

You can apply this algorithm to all image data types except complex and to 2D, 2.5D, and 3D images.

Special notes

The resulting image is, by default, a float type image.

To achieve 2.5D blurring (each slice of the volume is processed independently) of a 3D dataset, select Process each slice independently (2.5D) in the Laplacian dialog box (Figure 3).

References

Refer to the following references for more information about this algorithm:

Tony Lindeberg, "Linear Scale-Space I: Basic Theory," Geometry-Driven Diffusion in Computer Vision, Bart M. Ter Har Romeney, ed. (Dordrecht, The Netherlands: Kluwer Academic Publishers, 1994), pp. 1-38.

J. J. Koenderink, "The Structure of Images," Biol Cybern 50:363-370, 1984.

Raphael C. Gonzalez and Richard E. Woods, Digital Image Processing (Boston: Addison-Wesley, 1992).

Applying the Laplacian algorithm

To run this algorithm, complete the following steps:

  1. Select Algorithms > Filter > Laplacian. The Laplacian dialog box opens (Figure 3).
  2. Complete the fields in the dialog box.
  3. When complete, click OK. The algorithm begins to run.
A pop-up window appears with the status. The following message appears
"Calculating the Laplacian."
When the algorithm finishes, the pop-up window closes. Depending on whether you selected New Image or Replace Image, the results either appear in a new window or replace the image to which the algorithm was applied.
.
Figure 3. Laplacian dialog box
X Dimension
Specifies the standard deviation (SD) of Gaussian in the X direction.
DialogboxLaplacian.jpg


Y Dimension
Specifies the SD of Gaussian in the Y direction.
Z Dimension
Specifies the SD of Gaussian in the Z direction.
Amplification factor
Applies, by default, the classical laplacian factor of 1.0; values greater than 1.0 and less than 1.2 enable the laplacian to act as a high-pass, or high-boost, filter.
Use image resolutions to normalize Z scale
Normalizes the Gaussian to compensate for the difference if the voxel resolution is less than the voxel resolution inplane.
Process each edge independently (2.5D)
Blurs each slice of the dataset independently.
Output edge image
Produces a binary image that represents the edges defined by the 0 crossings of the laplacian
Threshold edge noise between <_> and <_>
Limits the threshold edge noise to the range that you specify between the 0 crossings of the laplacian; the default range is -10 to 10.
New image
Shows the results of the algorithm in a new image window.
Replace image
Replaces the current active image with the results of the algorithm.
Whole image
Applies the algorithm to the whole image.
VOI region(s)
Applies the algorithm to the volumes (regions) delineated by the VOIs.
OK
Applies the laplacian algorithm according to the specifications in this dialog box.
Cancel
Disregards any changes that you made in this dialog box and closes the dialog box.
Help
Displays online help for this dialog box.

See also:

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