math with images - uni siegen€¦ · c. wiktor lmn lehrstuhlseminar 24.06.20 1 image processing...
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![Page 1: Math with Images - Uni Siegen€¦ · C. Wiktor LMN Lehrstuhlseminar 24.06.20 1 Image Processing Math with Images • Image Compression • Changing the Size • Utilizing the Colors](https://reader033.vdocuments.net/reader033/viewer/2022053100/605b037f27edcc766b5fbdf9/html5/thumbnails/1.jpg)
C. Wiktor LMN Lehrstuhlseminar 24.06.20 1
Image ProcessingMath with Images
• Image Compression• Changing the Size• Utilizing the Colors Channels of an Image• Image Filters
![Page 2: Math with Images - Uni Siegen€¦ · C. Wiktor LMN Lehrstuhlseminar 24.06.20 1 Image Processing Math with Images • Image Compression • Changing the Size • Utilizing the Colors](https://reader033.vdocuments.net/reader033/viewer/2022053100/605b037f27edcc766b5fbdf9/html5/thumbnails/2.jpg)
C. Wiktor LMN Lehrstuhlseminar 24.06.20 2
Image Compression - Lossy Compression
• Discrete Cosine Transform(.jpeg, .heif (, video, sound, …)• 2n x 2n tiles approximates by
2D cosines
https://en.wikipedia.org/wiki/Image_compression
![Page 3: Math with Images - Uni Siegen€¦ · C. Wiktor LMN Lehrstuhlseminar 24.06.20 1 Image Processing Math with Images • Image Compression • Changing the Size • Utilizing the Colors](https://reader033.vdocuments.net/reader033/viewer/2022053100/605b037f27edcc766b5fbdf9/html5/thumbnails/3.jpg)
C. Wiktor LMN Lehrstuhlseminar 24.06.20 3
Image Compression - Lossy Compression
• Discrete Cosine Transform• Wavelet Transform (JPEG 2000)
https://en.wikipedia.org/wiki/Image_compression
![Page 4: Math with Images - Uni Siegen€¦ · C. Wiktor LMN Lehrstuhlseminar 24.06.20 1 Image Processing Math with Images • Image Compression • Changing the Size • Utilizing the Colors](https://reader033.vdocuments.net/reader033/viewer/2022053100/605b037f27edcc766b5fbdf9/html5/thumbnails/4.jpg)
C. Wiktor LMN Lehrstuhlseminar 24.06.20 4
Image Compression - Lossy Compression
• Discrete Cosine Transform• Wavelet Transform • Reducing the color space
• Reducing bit depth/color space vs. reduction to or summarizingoccuring colors
https://en.wikipedia.org/wiki/Color_spacehttps://en.wikipedia.org/wiki/Image_compression
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 5
Image Compression - Lossy Compression
• Discrete Cosine Transform• Wavelet Transform • Reducing the color space
• Reducing bit depth/color space vs. reduction to or summarizingoccuring colors
• (Dithering)
https://en.wikipedia.org/wiki/Color_quantizationhttps://en.wikipedia.org/wiki/Image_compression
Original 16 colors 16 colors + dithering
![Page 6: Math with Images - Uni Siegen€¦ · C. Wiktor LMN Lehrstuhlseminar 24.06.20 1 Image Processing Math with Images • Image Compression • Changing the Size • Utilizing the Colors](https://reader033.vdocuments.net/reader033/viewer/2022053100/605b037f27edcc766b5fbdf9/html5/thumbnails/6.jpg)
C. Wiktor LMN Lehrstuhlseminar 24.06.20 6
Image Compression - Lossy Compression
https://de.wikipedia.org/wiki/Dithering_(Bildbearbeitung)https://en.wikipedia.org/wiki/Image_compression
• Discrete Cosine Transform• Wavelet Transform • Reducing the color space
• Reducing bit depth/color space vs. reduction to or summarizingoccuring colors
• (Dithering)Original 16 colors 16 colors + dithering
![Page 7: Math with Images - Uni Siegen€¦ · C. Wiktor LMN Lehrstuhlseminar 24.06.20 1 Image Processing Math with Images • Image Compression • Changing the Size • Utilizing the Colors](https://reader033.vdocuments.net/reader033/viewer/2022053100/605b037f27edcc766b5fbdf9/html5/thumbnails/7.jpg)
C. Wiktor LMN Lehrstuhlseminar 24.06.20 7
Image Compression - Lossy Compression
• Discrete Cosine Transform• Wavelet Transform• Reducing the color space• Chroma subsampling (JPEG)
• Stronger reduction of color informationover a reduction intensity information
https://en.wikipedia.org/wiki/Image_compression
![Page 8: Math with Images - Uni Siegen€¦ · C. Wiktor LMN Lehrstuhlseminar 24.06.20 1 Image Processing Math with Images • Image Compression • Changing the Size • Utilizing the Colors](https://reader033.vdocuments.net/reader033/viewer/2022053100/605b037f27edcc766b5fbdf9/html5/thumbnails/8.jpg)
C. Wiktor LMN Lehrstuhlseminar 24.06.20 8
Image Compression - Lossy Compression
• Discrete Cosine Transform• Wavelet Transform• Reducing the color space• Chroma subsampling• Fractal compression
• Compressed self-similar (reoccuring) parts saved once
https://en.wikipedia.org/wiki/Image_compression
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 9
Image Compression - Lossless Compression
• Run-length encoding (GIF)• Repeated lines saved once
https://en.wikipedia.org/wiki/Image_compression
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 10
Image Compression - Lossless Compression
• Run-length encoding• Differential Pulse Code Modulation
• Calculating and saving the difference of one part of the signal with another part
https://en.wikipedia.org/wiki/Image_compression
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 11
Image Compression - Lossless Compression
• Run-length encoding• Differential Pulse Code Modulation• Entropy encoding
• Prefix code for each „unique symbol“ in signal, saving prefix code sequence• Basis for arithmetic coding and Huffman coding
https://en.wikipedia.org/wiki/Image_compression
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 12
Image Compression - Lossless Compression
• Run-length encoding• Differential Pulse Code Modulation• Entropy encoding• Lempel–Ziv–Welch (GIF, TIFF)
• Assemble Dictionary of signal sequences in input and where to find them
https://en.wikipedia.org/wiki/Image_compression
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 13
Image Compression - Lossless Compression
• Run-length encoding• Differential Pulse Code Modulation• Entropy encoding• Lempel–Ziv–Welch• DEFLATE (.png, .mng, .tiff)
• Lempel–Ziv–Storer–Szymanski + Hoffmann encoding• Dictionary method + entropy encoding
https://en.wikipedia.org/wiki/Image_compression
![Page 14: Math with Images - Uni Siegen€¦ · C. Wiktor LMN Lehrstuhlseminar 24.06.20 1 Image Processing Math with Images • Image Compression • Changing the Size • Utilizing the Colors](https://reader033.vdocuments.net/reader033/viewer/2022053100/605b037f27edcc766b5fbdf9/html5/thumbnails/14.jpg)
C. Wiktor LMN Lehrstuhlseminar 24.06.20 14
Image Compression - Lossless Compression
• Run-length encoding• Differential Pulse Code Modulation• Entropy encoding• Lempel–Ziv–Welch• DEFLATE• Chain code
• Saves outline of area with same greyvalue
https://en.wikipedia.org/wiki/Image_compression
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 15
Changing the Image Size - Pixel based Images
• Several typical algorithms available• Bilinear and Bicubic• Nearest Neighbor
Functions in FIJI/ImageJ to resize images• Image Adjust Size…• Image Scale…
https://en.wikipedia.org/wiki/Bicubic_interpolationhttps://en.wikipedia.org/wiki/Image_scaling
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 16
Changing the Image Size - Pixel based Images
• Several typical algorithms available• Bilinear and Bicubic
• Extrapolates local image intensities• Can extrapolate curved lines• May introduce artifacts
3dmix.comhttps://en.wikipedia.org/wiki/Image_scaling
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 17
Changing the Image Size - Pixel based Images
• Several typical algorithms available• Bilinear and Bicubic• Nearest Neighbor
• Preserves image intensities andedges if image enlarged by n
• Can otherwise also create artifacts• Bad edge preservation when
reducing size• Lower pixel intensities due to
rounding down
3dmix.comhttps://en.wikipedia.org/wiki/Image_scaling
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Changing the Image Size - Pixel based Images
• Several typical algorithms available• Bilinear and Bicubic• Nearest Neighbor• Choose according to purpose/image• Always check for artifacts (at the
pixel scale)!
3dmix.comhttps://en.wikipedia.org/wiki/Image_scaling
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 19
Changing the Image Size - Vector based Images
https://de.wikipedia.org/wiki/Vektorgrafik
• All Image information strored as primitives such aslines, circles, splines, etc. (essentially functions)
• Supported by .svg, .eps, .wmf, .ai, .pdf• Infinitely scalable• Concept also available in 3D renderings
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Changing the Image Size - Best practices
• Ideally record images of carefully chosen areas and with enough pixels(min 4M pixels!)
• Avoid small changes in image size• Change image size as few times as possible• Use Corel Draw, since pixelated images intensities are only extrapolated
once when image is saved in pixelated format• Or save as vector file
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 21
• Up to 3 greyscale maps/images remain rather interpretable• Illustration of change between two points in time between two greyscale images
Utilizing the Color Channels of an Image
Development of [111] texture in Pt thin film due to heating
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 22
• Up to 3 greyscale maps/images remain rather interpretable• Illustration of change between two points in time between two greyscale images• RGB channels (e.g. for three overlapping images/EDX maps)
• Maximize contrast vs quantified contrast?• Apparent intesity of different colors?
• Easiest to stick with greyscale images• Adjustments have to be stated!
Utilizing the Color Channels of an Image
Functions in FIJI/ImageJ to separate/combineimages• Image Color Merge/Split Channels• Image Stacks… Z Project• Process Image Calculator
Up to 7 color channels availableChannel operations also possible with stacks
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Image Filters - Convolutions for Noise Reduction
• At each pixel a new value is calculated based on the surrounding pixels
• #
Original noisyimage
stackexchange.comscipy-lectures.org/intro/scipy/auto_examples/plot_image_filters.html
Median ofintensities in 5x5 matrix
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Image Filters - Convolution for Edge Detection (Sobel Filter)
• Convolution with matrices for x and y direction
medium.com
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• Theshold selcted visually or basedon histogram
• Several automatic methods availblein FIJI/ImageJ
• Automatic particle anaylsis availableas well
Image Filters – Threshold based Segmentation
imagej.nih.gov
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Image Filters - Fourier Filtering
medium.com
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C. Wiktor LMN Lehrstuhlseminar 24.06.20 27
The Fourier Transformation
f(x) = sin (x)
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The Fourier Transformation
f(x) = sin (8*x)
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The Fourier Transformation
f(x) = sin (x) + sin (8*x)
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The Fourier Transformation
bonedo.de
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Image Filters - Fourier Filtering
B. Mei, ACS Catal. 3 2013 3041−3049.
Original Low Pass Filter Low Pass Filter(Overdone)
High and Low Pass Filter
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Image Filters - Fourier Filtering
B. Mei, ACS Catal. 3 2013 3041−3049.
Wedge Shaped FilterJust Spots
All masks created andapplied in GMS3
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Image Filters - Fourier Filtering
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The World of Scripting – Python ftw!
• All the things above!• Summing up images after aligning
them via cross-correlation!• Zoom videos consisting of extrapolated
images based on images recorded at fixed magnifications!
• Dynamic scale bars!• Create your own noise removal
techniques!• Extracting data from in situ image
series!• Data visualization!• Combining image series into single
images in creative ways!• There are no limits!
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Thank you for your attention!