Bioimage Computing Overview

• Bioimage computing leverages machine learning, computer vision, and image processing.
• It enhances medical image diagnosis.
• Aids clinical decision support systems.
• Improves image quality.

Syllabus Breakdown

• Reconstruction: Focuses on mathematical models for image regularity.
  • Covers random fields.
  • Includes practical data sampling and acquisition schemes.
• Restoration: Employs deconvolution and degradation models for corrupted and missing data.
  • Utilizes Bayesian graphical modeling and inference.
  • Explores regression methods for bioimage filtering.
• Image Segmentation, Delineation & Classification: Clustering, graph partitioning and classification are used.
  • Includes mixture models, expectation maximization, variational methods.
  • Applies geometric and statistical modeling, and computer-aided diagnosis.
• Registration: Focuses on deformation models and optimization algorithms.
  • Includes 2D-3D and multi-modal registration.

Course Logistics

• Instructor is Angshuman Paul with contact at [email protected].
• Class hours are:
  • Monday: 3 PM-3.50 PM
  • Wednesday: 3 PM-3.50 PM
  • Thursday: 3 PM-3.50 PM

Evaluation Components

• The evaluation is tentatively split into:
  • Quiz (30%).
  • Viva (30%).
  • Minor (40%).

Study Materials

• Core books include:
  • "Fundamentals of Light Microscopy and Electronic Imaging" by Murphy D.B. (2nd edition, John Wiley & Sons, Inc.).
  • "Pattern Recognition and Machine Learning" by Bishop, C. (2006, Springer).
  • Additional online materials may be introduced.

Prerequisites

• Requires a basic understanding of mathematics.

Medical Images Context

• Most medical images result from electromagnetic (EM) waves, such as:
  • X-rays, CT scans.
  • MRI.
  • Histopathology images and optical microscopy images.
  • PET.
  • OCT.
• Some medical images use sound waves, like ultrasound.

Importance of Bioimage Computing

• Decision support systems offer:
  • Improved diagnostic accuracy.
  • Automated diagnosis.
  • Enhanced image quality.
• Bioimage computing enables:
  • Faster processing.
  • Telemedicine applications.
  • More affordable health care.

Current Status and Challenges

• The field has seen significant progress and achieved human-level or superhuman accuracy
• Decision support systems now have FDA approval
• Current challenges in bioimage informatics:
  • Generalizability.
  • Explainability.
  • Cost of annotation.
  • High computational requirements.

Why Study Bioimage Computing?

• Learn classical and state-of-the-art approaches.
• Improve existing methodologies.
• Push the boundaries of current capabilities.
• Design innovative solutions.
• Address critical challenges in the field.
• Apply understandings and innovations to other fields.

Probability and Uncertainty

• The real world is full of uncertainties; this is an important consideration for many fields
• It is very hard to model everything, and so abstractions are frequently required

Experiments

• Deterministic experiments have known outcomes.
  • For example, an object released from a roof will move downwards.
• Random experiments outcomes are unknown beforehand.
  • For example, rolling a dice.

Sample Space

• The set of possible outcomes.
• For rolling dice, it is {1, 2, 3, 4, 5, 6.}.
• Each outcome is a sample point.
• Sample spaces can be finite like dice, or infinite like the amount of rainfall.

Event

• It is any subset of the sample space.
• For example, rolling a dice can have the event A = { 1, 2}

Random Variables

• Used in probability.
• Describes numerical outcomes of an experiment.
• A function that assign numerical values of an experiment.
• Discrete random variables example: {sunny, rainy, cloudy}.
• Continuous random variables e.g. measuring temperatures: [6.7°, 46.2°].

Probability of an Event

• P(A) = (Number of elements in set A) / (Number of elements in the sample space S)
• Another form: P(A) = (Number of favourable outcomes) / (Total number of outcomes)
• For example, the probability of resulting an odd number from throwing dice = {1,3,5} = 0.5 6
• Limitation: Requires equally likely outcomes.

Frequentist Approach to Probability

• In experiments performed "n" times, where event A occurs "n(A)" times
• Relative frequency: fr(A) = n(A)/n.
• Probability: = lim fr(A) = lim n(A)/n, where n trends to infinity.

Probability Measures

• Probability: P(A) or probability function P(.) assigns a probability measure to an event A. P(A), measures the chance event A occurs.

Characteristics of Probability

• P(A) has to be between 0 and 1.
• P(Null) = 0.
• P(S) is 1.

Probability Disjoint Properties

• Countable sequence of disjoint events like: P(A₁ U A2 U ... U An) = P(A₁) + P(A₂) + ... + P(An)
• Mutaully exclusive: Events don't occur simultaneously.
• Example: Rolling dice is disjoint, can't roll a 1 and a 2 at the same time
• S = AU Ac
• where P(S) = 1 = P(AU Ac) = + P(A)+ P(Ac)

Probability Adition Rule

• P(A U B) = P(A) + P(B) - P(A ∩ B)

Revisiting Random Variables

• A list containing (P1, P2, ..., Pk)
• Often represented as a histogram

Continous Random Variables

• Represented by f(v)
• Area under the curve is 1
• f(v) ≥ 0 at all points where v is a continous random variable

Conditional Probability

• Conditional probability: P(SP|NW)
• Equation: P(SP|NW) = P(NW|SP) P(SP) = P(SP∩NW)

Bayes' Theorem

P(A|B) = P(A∩B) = P(B|A) P(A) P(B) P(B)

• This decomposes into P(Cause | Effect) = P(Effect|Cause) P(Cause) P(Effect)

• In simpler terms where E may be caused by c₁ or c₂, then can use the following P(c1|e₁) + P(c2|e₁) = 1

Independent Events

• Defined as: P(A|B) = P(A)
• Another form: P(A ∩ B) = P(A)P(B)

Joint Probability Distribution

• A joint probability distribution of X and Y
• Probability distribution on all possible pairs of outputs
• Weather and Power cut

Chain Rule

• Probability rule where:
• P(A ∩ An-1∩∩ A₁) = P (An|An-1∩∩ A₁) P(An-1∩∩ A₁) … …
• Similarly, P(An-1∩ An-2∩∩ A₁) = P(An-1|An-2∩∩A₁) P(An-2∩∩ A1) …
• For 3 events, the formula is P(A ∩ An-1∩∩A₁) = P (An|An-1∩∩A₁) P(An-1|An-2∩∩ A₁) P(An-2|An-3∩∩ A₁) ...P(A1) …

Inference by enumeration

• Any proposition, add all the boxes where the proposition is true

• COVID data can be arranged like:

• Covid with a Cough, No fever =0.21

• Acovid with Cough, No fever = 0.09

• With the equation to find:

• P(¬covid¬fever) =P(¬covid ∩¬fever) P(¬fever)

Independent Events

• To deal with Fever, Cough, Covid, and Internet Speed (I_Sp)
• P is P(Fever, Cough, Covid, I_Sp) = P(Fever, Cough, Covid) P(I_Sp)

What is Clustering

Groups are more similar to each other than the sample in other groups

Clustering Techniques

• Centroid Models -> k-Means, k-medoid
• Graph-based -> Spectral clustering
• Distribtuion -> Gaussian Mixture Models
• Density -> DBSCAN
• Connectivity -> Hierarchical Clustering
• Neutral -> Self-organizing map

K-means Clustering

• Step 1: Determine the "m" clusters
• Step 2: There is a random intialiazation value to begin
• Step 3: Assign samples from the closest cluster to the value
• Step 4: Determien the cluster mean. Redo step 3 if necessary, check change is significant in new sample

Limitations of K-means

• "K" can be hard determine properly
• Sensitive to outliers meaning value is affected by rogue signals
• Random initialisation can lead to varying results

K-medoids

• Rather than random centroids, "medoids" are selected; the sample closest to the cluster
• Steps as follows"
• Create datapoints with various samples from the dataset
• Random assigin the medoids to the samples
• Determine all other nearest data point/ medoid to assgin to medaid cluster
• Calculate the distance from sample to the point - Sum of all distances is the cost

Challenges of K-medoids

• If new cost > old cost, discard new one
• Can repeat, or converges in sample and values

DBSCAN

• Use Density
• Apply desc size or parameter • Put it each time across • If m number within "i" area. Then that’s the corepoint. • Assign cluster in corepoint • Redo the operation

DBSCAN Adevantages/ Disadvantages

• No need for a priori knowledge of clusters
• The non-core point will gets included to green, as not not a stable area to form a cluster

To Perform DBSCAN

• 1. Perform density based clustering of application with noise
• S set data
• 2. Choose a value of epsilon and radius in the model
• Look for poiunts which reside within disc, x1

3. The Ai cannot be lower that value given for the data, this is called core value
4. Perform unoin operation, with no more unions are possibble

• mutalling non overlapping

Variance Describes to the spread of data. Variance = E[(X – μ)²]

Covariance

Pointwise products with the data. Shows joint trend where an increase in a value to also increase.

Joint Matrix

Σ = var(X). cov(X, Y)) (cov(X, Y). var(Y) )

• Describes joint variance, if points are trending positive or negative

Gaussian Mixture Models

p(xa|μ, σ) = 1 e √2πσ

• (xa - u)2 / 2σ2
• Values closer to centre μ, are most likley to have a contributing factor

Steps to clustering to GMM

• Take random samples from what given, and assign it in gaussian space • check which Gaussian point to use •Recaculare mu sigman pi to the max of the likehood • Then repeat steps 2-4 where it goes for a termination criteria

1. Can terimate the data
2. when for each cluster
3. Do not change by a significantly for a few epochs

Using Baysian Theorem

•	To know the likelynesess of  a class, check following

• Σ=1 in first equation
• Each Gausian, can be the cluster I belongs

Soft decision vs Hard Decision

Take hard decision which Gaussial, which pont is in
But in a soft we apply probability

• Look to max the log-likelihood function

Expectation Maxima-tion

• R randomalise mu sigma
• E step, check each point woth K Gaussinas
• m Step, Recaulcalre mu, sigma. Pr for each cluster

Classification Techniques: K- Nearest Neighbours

1. Plot the raining data
2. Plot the test data
3. k nearest neighours
4. Find k number, label occuring the most , like in 1.0

Types of Nodes in Trees

• Decision Nodes - Has split to the various data
• Steps on how to build a split

1. Want leaf noe to contain data of one clssa only to increasse homegniety
2. from tree node we want nodesto become homoenus Goal is to reach pure point where you have data of single point

• As impuiryt increases, entrophy or data increases

In the context of Rolling a Dice

• The outcome is number < 3
• A= { 1, 2}

Chain Function and formula

• If a1…… a2 are even
• P (ala, A1) then
• Pala.. A1 Ala1) P (A2| a1……
• Pa.. A1) = 1…… AA1 . P(A1| A2 AA P …)
• For Rolling the Dis Ex. if we rolling of lice 4 times, the probably is the roll of Dice is Mutualling

Random Forerest

• How many trees decide to be
• Splititning of the nide, such as enteropoy, varaiance
• Formularizing a tree, which is bootstrap of treei,

Image Regration

• Find a trans, to have every ppixel to have a correnspondding pixel in the image Input iamge . terage inmage

Image Landmark-based Regration

• The trans has landmark pO, to have reference images

  • Can be trans,.roat , etc

• Formula for a new inmage

• A : (x,y) To a a(x,y)

• A’ = T (a)

  Transformation ^ = B-a N = b = E B / N A=1 A

For continours Feature for Tree

Check the data

• P (fever | covid, cough() = P (fever | condidion()
• The Feaute, covid conditly, Independent with cough

Graphiacal REpresntative

Whatis the poiny

• Use to Under standing

Limitation

• A system with Many causes and Effect we ahvveto manaitina large
• Independent Eventa P = (Au 4 A), u An) Pala, V V, A1+)…..p a v
  • Disjonit mutual exclusice

If one want to find the proabolity  fever
  - P(fever. couvid cough) 24
How  to

• We need it in foramtation
• 8 (7 par) If the parmater is low, is to store than aboeve

Bayesion Theerom

P{ a/6) > = Plb] A) Pala}P(a) B

Random Desction

• How to store tabele, or more efficicen
• A-H for random inforamatiorn?
• More the par, more are the prt
• It is in in our mind

In a conditon

P fever cony

Conidition indepeindtance

• fever a cough or probabitlic

Explore probability concepts, random variables, and their applications in real-world modeling. Questions cover deterministic experiments, sample spaces, continuous random variables, and probability calculations. Includes conditional probability scenarios and matching concepts.