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---
title: Image math
layout: page
---
layout: module
prerequisites:
- "TODO"
objectives:
- "TODO"
motivation: >
TODO
concept_map: >
graph TD
II("Intensity Image") --> CV("Convolution")
KN("Kernel") --> CV
KN -- is --> SI("Small Image")
CV --> FI("Filtered Image")
SI --> SZ("Size")
SI --> PV("Pixel Values")
# figure: /figures/binarization.png
# figure_legend: Image before and after binarization by applying a threshold.
activity_preface: >
### Activity: Explore convolution filters
* Open image: xy_8bit__nuclei_noisy_different_intensity.tif
* Try the result of different convolution filters, e.g.
* https://en.wikipedia.org/wiki/Kernel_(image_processing)
* Mean filter
## Convolution filters
* Gaussian blur
<img src='https://g.gravizo.com/svg?
digraph G {
shift [fontcolor=white,color=white];
"intensity image" -> "convolution" -> "filtered image";
"small image" -> size;
"small image" -> "pixel values";
"kernel" -> "small image" [label=" is"];
"kernel" -> "convolution";
}
'/>
* Edge detection
### Activity: Explore convolution filters
* Appreciate that the results are (slightly) wrong within the 8-bit range of the input image.
* Open image: xy_8bit__nuclei_noisy_different_intensity.tif
* Try the result of different convolution filters, e.g.
* https://en.wikipedia.org/wiki/Kernel_(image_processing)
* Mean filter
* Gaussian blur
* Edge detection
* Appreciate that the results are (slightly) wrong within the 8-bit range of the input image.
### Activity: Use mean filter to facilitate image segmentation
### Activity: Use mean filter to facilitate image segmentation
* Open image: xy_8bit__nuclei_noisy_different_intensity.tif
* Open image: xy_8bit__nuclei_noisy_different_intensity.tif
* Appreciate that you cannot readily threshold the image
* Apply a mean filter
* Threshold the filtered image
* Appreciate that you cannot readily threshold the image
### Formative assessment
* Apply a mean filter
* Draw the kernel of a 3x3 mean filter.
* Draw three different kernels that enhance edges.
* Threshold the filtered image
### Learn more
activities:
# "ImageJ GUI": "binarization/activities/binarization_imagejgui.md"
# "ImageJ Macro": "binarization/activities/binarization_imagejmacro.md"
# "Jython": "binarization/activities/binarization_jython.md"
# "MATLAB": "binarization/activities/binarization_matlab.md"
# "KNIME": "binarization/activities/binarization_knime.md"
* https://en.wikipedia.org/wiki/Kernel_(image_processing)
exercises_preface: >
### Formative assessment
* Draw the kernel of a 3x3 mean filter.
* Draw three different kernels that enhance edges.
exercises:
# "ImageJ GUI": "binarization/exercises/binarization_imagejgui.md"
# "ImageJ Macro": "binarization/exercises/binarization_imagejmacro.md"
# "Jython": "binarization/exercises/binarization_jython.md"
# "MATLAB": "binarization/exercises/binarization_matlab.md"
learn_next:
- "TODO"
external_links:
- "[Wikipedia: Kernels for Image Processing](https://en.wikipedia.org/wiki/Kernel_(image_processing))"
---