The mathematics of image analysis

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00:00:00 Welcome
00:01:41 The math(ematics) of image analysis
00:01:53 Abstract
00:02:45 Agenda
00:03:12 Most important questions – the big picture
00:05:14 O2Q
00:06:00 The ‘smaller’ picture
00:07:32 Basic principles of image analysis
00:08:15 Before the analysis – taking the sample
00:09:12 Taking a (hopefully representative?) sampleHopelessly unrepresentative?
00:11:49 The sample
00:12:28 Image Analysis – basics and expanded from CarltonFull reference later
00:12:56 Image acquisition – the key part
00:14:40 Eric Pirard Personal communication October 5th, 2010: 06:21 AM
00:15:37 Resolution - Definition
00:16:15 Lower limit - diffraction
00:16:48 Numerical Aperture (N.A.)
00:17:02 Limits of resolution
00:17:54 Limits of resolution
00:18:39 Untitled
00:19:15 Heywood’s warning
00:20:16 Defeating the Abbe limit
00:20:41 Nobel Prize in Chemistry - 2014
00:21:06 Possibilities and Limitations
00:21:43 Magnification
00:22:24 Depth of field
00:23:02 Depth of field
00:23:35 Depth of field
00:24:01 Focus
00:24:59 Object extraction
00:25:35 Image J – simple example
00:26:05 Isolation of image from background – 256 levels
00:26:35 Noise removal
00:27:27 Binarization
00:28:08 Variable background – Image J
00:28:41 Variable background
00:29:25 Digitization – care! From ISO 9276-6Pixel resolution and 16:9 display…
00:30:33 Particle orientation with respect to x- and y-axes
00:31:46 Edge and perimeter isolation: 8-neighbor
00:32:10 Thresholding
00:33:18 Object Extraction - Thresholding
00:34:15 Thresholding
00:34:46 Erosion-dilation
00:35:47 Hole filling
00:36:44 How do we count the number of particles?
00:37:35 De-agglomeration – in software!Processing (Erosion-Dilation)Post-processing (Circularity)
00:38:37 Original image (10MB picture)
00:39:08 Decide which part of the image to analyze
00:39:44 Extract the sample
00:40:00 Process 1 – negative imageGrey scale (256 levels)
00:40:16 Digitize (2 colors)
00:40:24 Process 1 – negative imageGrey scale (256 levels)
00:40:28 Digitize (2 colors)
00:40:34 The original and processed image overlaid
00:41:12 ImageJ – jpeg warning (page 57 of manual)
00:41:42 What have we lost?
00:42:00 The lost tree (increasing brightness and contrast)
00:42:18 Note these ‘particles’ – appear as an aggregateLet’s carefully examine the original 10 MB photograph
00:43:02 Threshold – automatic setting
00:43:30 Threshold
00:43:50 Threshold
00:44:15 Process the data (1269 particles) – automatic threshold: using 1 mm/pixel for convenience
00:44:45 Lots of data per particle Size and shape on the same plot
00:45:09 Threshold 25 (359 particles)
00:45:50 Compare threshold results for 1269 and 359 particles Number distribution
00:46:07 Shape information – aspect ratio - distribution
00:46:36 Circularity - distribution
00:46:46 The Tetris effect – take care when you’re at the lower limit (low numbers of pixels/small particles)
00:47:46 So what does that give us?
00:47:55 So, we have binary, digitized images of particlesPost-processing – generation of shape parameters
00:48:29 And this leads to these image analysis parameters….G Yamate, J D Stockham “Sizing particles using the microscope” Chapter 3 of J D Stockham, E G Fochtman (Eds.) Particle Size Analysis Ann Arbor Science Publishers Inc (1977) ISBN: 0 250 40189 4
00:48:51 A couple of common parameters
00:49:29 Area-volume
00:49:45 Post processing – the results – 2-D descriptorsAdditional complexity – and distributions….
00:50:07 International Standards – documentaryWhere are the materials standards?
00:50:18 ISO9276-6
00:50:22 ISO9276-6
00:50:54 ASTM F1877 - 05(2010)
00:51:20 We’ll end with Heywood’s warning
00:51:40 References
00:52:20 References
00:52:42 Past (relevant?) webinars
00:53:29 Thank you!
00:54:19 Thank you for your attentionAny questions?
01:03:04 Contact Information
Thresholding, dilation, erosion, reporting - these are some of the terms used in image analysis. We'll explain some of the mathematics used in converting an image into size and shape information.