Quantitative Big Imaging

Kevin Mader
07 April 2016

ETHZ: 227-0966-00L

Analysis of Complex Objects

Course Outline

  • 25th February - Introduction and Workflows
  • 3rd March - Image Enhancement (A. Kaestner)
  • 10th March - Basic Segmentation, Discrete Binary Structures
  • 17th March - Advanced Segmentation
  • 24th March - Analyzing Single Objects
  • 7th April - Analyzing Complex Objects
  • 14th April - Spatial Distribution
  • 21st April - Statistics and Reproducibility
  • 28th April - Dynamic Experiments
  • 12th May - Scaling Up / Big Data
  • 19th May - Guest Lecture - High Content Screening
  • 26th May - Guest Lecture - Machine Learning / Deep Learning and More Advanced Approaches
  • 2nd June - Project Presentations

Literature / Useful References

Books

  • Jean Claude, Morphometry with R
  • Online through ETHZ
  • Buy it
  • John C. Russ, “The Image Processing Handbook”,(Boca Raton, CRC Press)
  • Available online within domain ethz.ch (or proxy.ethz.ch / public VPN)

Papers / Sites

  • Thickness
    • [1] Hildebrand, T., & Ruegsegger, P. (1997). A new method for the model-independent assessment of thickness in three-dimensional images. Journal of Microscopy, 185(1), 67–75. doi:10.1046/j.1365-2818.1997.1340694.x
  • Curvature

Previously on QBI ...

  • Image Enhancment
    • Highlighting the contrast of interest in images
    • Minimizing Noise
  • Segmentation
    • Understanding value histograms
    • Dealing with multi-valued data
  • Automatic Methods
    • Hysteresis Method, K-Means Analysis
  • Regions of Interest
    • Contouring
  • Component Labeling
  • Single Shape Analysis

Outline

  • Motivation (Why and How?)
  • What are Distance Maps?
  • Skeletons
    • Tortuosity
  • What are thickness maps?
    • Thickness with Skeletons
  • Watershed Segmentation
    • Connected Objects
  • Curvature
    • Characteristic Shapes

Learning Objectives

Motivation (Why and How?)

  • How do we measure distances between many objects?
  • How can we extract topology of a structure?

  • How can we measure sizes in complicated objects?

  • How do we measure sizes relavant for diffusion or other local processes?

  • How do we identify seperate objects when they are connected?

  • How do we investigate surfaces in more detail and their shape?

  • How can we compare shape of complex objects when they grow?

    • Are there characteristic shape metrics?

What did we want in the first place

To simplify our data, but an ellipse model is too simple for many shapes

So while bounding box and ellipse-based models are useful for many object and cells, they do a very poor job with the sample below.

Single Cell

Why

  • We assume an entity consists of connected pixels (wrong)
  • We assume the objects are well modeled by an ellipse (also wrong)

What to do?

  • Is it 3 connected objects which should all be analzed seperately?
  • If we could divide it, we could then analyze each spart as an ellipse
  • Is it one network of objects and we want to know about the constrictions?
  • Is it a cell or organelle with docking sites for cell?
  • Neither extents nor anisotropy are very meaningful, we need a more specific metric

Distance Maps: What are they

A map (or image) of distances. Each point in the map is the distance that point is from a given feature of interest (surface of an object, ROI, center of object, etc)

Simple Circles

Definition

If we start with an image as a collection of points divided into two categories

  • \( Im(x,y)= \) {Foreground, Background}
  • We can define a distance map operator (\( dist \)) that transforms the image into a distance map

\[ dist(\vec{x}) = \textrm{min}(||\vec{x}-\vec{y}|| \forall \vec{y} \in \textrm{Background}) \]

We will use Euclidean distance \( ||\vec{x}-\vec{y}|| \) for this class but there are other metrics which make sense when dealing with other types of data like Manhattan/City-block or weighted metrics.

Distance Maps: Types

Using this rule a distance map can be made for the euclidean metric