Quantitative Big Imaging

Many Objects and Distributions

ETHZ: 227-0966-00L

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Course Outline

Literature / Useful References

Books

Literature (Continued)

Papers / Sites

Previously on QBI …

Outline

Motivation (Why and How?)

Global Enviroment

Metrics

We examine a number of different metrics in this lecture and additionally to classifying them as Local and Global we can define them as point and voxel-based operations.

Point Operations

x y z
2 3 4
1 1 3
1 0 4
0 0 4

Voxel Operation

What do we start with?

Going back to our original cell image

  1. We have been able to get rid of the noise in the image and find all the cells (lecture 2-4)
  2. We have analyzed the shape of the cells using the shape tensor (lecture 5)
  3. We even separated cells joined together using Watershed (lecture 6)

We can characterize the sample and the average and standard deviations of volume, orientation, surface area, and other metrics

Motivation (Why and How?)

With all of these images, the first step is always to understand exactly what we are trying to learn from our images.

All Cells

All Cells

  1. We want to know how many cells are alive
  1. We want to know where the cells are alive or most densely packed

Motivation (continued)

All Cells

All Cells

  1. We want to know how the cells are communicating

Motivation (continued)

All Cells

All Cells

  1. We want to know how the cells are nourished

So what do we still need

  1. A way for counting cells in a region and estimating density without creating arbitrary boxes
  2. A way for finding out how many cells are near a given cell, it’s nearest neighbors
  3. A way for quantifying how far apart cells are and then comparing different regions within a sample
  4. A way for quantifying and comparing orientations

What would be really great?

A tool which could be adapted to answering a large variety of problems - multiple types of structures - multiple phases

Destructive Measurements

With most imaging techniques and sample types, the task of measurement itself impacts the sample. - Even techniques like X-ray tomography which claim to be non-destructive still impart significant to lethal doses of X-ray radition for high resolution imaging - Electron microscopy, auto-tome-based methods, histology are all markedly more destructive and make longitudinal studies impossible - Even when such measurements are possible - Registration can be a difficult task and introduce artifacts

Why is this important?

Ok, so now what?

Smaller Region

Smaller Region

\[ \downarrow \]

x y vx vy
20.19 10.69 -0.95 -0.30
20.19 10.69 0.30 -0.95
293.08 13.18 -0.50 0.86
293.08 13.18 -0.86 -0.50
243.81 14.23 0.68 0.74
243.81 14.23 -0.74 0.68

\[ \cdots \]

So if we want to know the the mean or standard deviations of the position or orientations we can analyze them easily.

Min. 1st Qu. Median Mean 3rd Qu. Max.
x 6.90 215.70 280.50 258.20 339.00 406.50
y 10.69 111.60 221.00 208.60 312.50 395.20
Length 1.06 1.57 1.95 2.08 2.41 4.33
vx -1.00 -0.94 -0.70 -0.42 0.07 0.71
vy -1.00 -0.70 0.02 0.04 0.71 1.00
Theta -180.00 -134.10 -0.50 -4.67 130.60 177.70

Simple Statistics

When given a group of data, it is common to take a mean value since this is easy. The mean bone thickness is 0.3mm. This is particularly relevant for groups with many samples because the mean is much smaller than all of the individual points.

but means can lie

some means are not very useful