# Quantitative Big Imaging

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

### Books

• Jean Claude, Morphometry with R
• Online through ETHZ
• 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

### 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.

### 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)

### 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