Medical Image Computing
Tutorial 1
Theoretical part (based on exam Q1 from 2005)
Visualization of
of Medical
Medical Images
Images
11
Visualization
1. aA 3D MR volume is rendered using an image-order volume rendering algorithm.
A 3D
3D MR
MR v
Mathematics for Inference and Machine Learning
Tutorial 2
1. Vector Calculus.
Consider the following functions
f1 (x) = sin(x1 ) cos(x2 ) , x R2
f2 (x, y) = x> y , x, y Rn
f3 (x) = xx> ,
x Rn
(a) What are the dimensions of
fi
x
(1)
(2)
(3)
?
(b) Compute t
Chapter 2
Part II: Feature Extraction
2.1
Decompositions
In this chapter we will discuss about the use of linear algebra of vectors and matrices
in order to define basic feature extraction and dimensionality reduction methodologies. In this context, we wi
Medical Image Computing:
Segmentation
Professor Daniel Rueckert
Some slides adapted from
Maximilian Baust & Nassir
Navab
Overview: Medical image
segmentation
Definition
Purpose
Challenges
Evaluation
Algorithms
Model-based
Intensity-based
Atlas-based
So
October 20, 2016
Department of Computing
CO424H Learning in Autonomous Systems (LIAS) Dr Aldo Faisal
Assessed coursework
To be returned via CATE as indicated online.
Your coursework should contain: brief analytical derivations and calculations or short pi
CO316 Computer Vision
Lecture 10 Modelling for
Vision
Su-Lin Lee, PhD
[email protected]
Prof Guang-Zhong Yang
[email protected]
The Hamlyn Centre
for Robotic Surgery
Contents
Physics-based modelling
Active contours
Geometric modelling
Affine
CO316 Computer Vision
Lecture 6 The Hough
Transform
Su-Lin Lee, PhD
[email protected]
Prof Guang-Zhong Yang
[email protected]
The Hamlyn Centre
for Robotic Surgery
Contents
Introduction to the Hough Transform
A mathematical interlude
The Wal
C477: Computing for Optimal Decisions
Tutorial 1: Convexity
Exercise 1. Intersections & Unions of Convex Sets
(a) Show that if C1 and C2 are convex then their intersection S1 is also convex:
\
S1 = C1 C2 .
(b) Show that if Ci , i = 1, . . . , n are convex
C477: First Order Methods
Ruth Misener
[email protected]
Panos Parpas
[email protected]
Computational Optimisation Group
Department of Computing
24 & 31 Oct 2016
Misener & Parpas
C477: First Order Methods
24 & 31 Oct 2016
1 / 33
Outline
Topic
EE4»40
EEQCS7-2
EE93020
IMPERIAL COLLEGE LONDON
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING
EXAMINATIONS 2011
M80 and EEEilSE PART IV: MEng and A081
Corrected Copy
C(Lr(c)
INFORMATION THEORY
Wednesday, 18 May 10:00 am
Time allowed: 3:00 hours
Ther
Information Theory
Problem Sheet 1
(Most questions are from Cover & Thomas, the corresponding question numbers (as in 1st ed.) are given in brackets at the start of the question)
Notation: x, x, X are scalar, vector and matrix random variables respectivel
Paper Number(s): E4.40
C5.27
SO20
ISE4.51
IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE
UNIVERSITY OF LONDON
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING
EXAMINATIONS 2006
MSc and EEE/ISE PART IV: MEng and ACGI
INFORMATION THEORY
Wednesday,
Paper Number(_s): £4.40
C527
8020
ISE4.51
IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE
UNIVERSITY OF LONDON
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING
EXAMINATIONS 2008
MSc and EEEIISE PART IV: MEng and ACGI
INFORMATION THEORY
Monday, 12
C477: Computing for Optimal Decisions
Tutorial 7: Constrained Optimisation Optimality
Conditions
Exercise 1. Consider the problem,
min kx x0 k2
s.t. kxk2 = 9,
where x0 = [1, 3]> .
(a) Find all the points satisfying the Lagrange condition for the problem.
C477: Computing for Optimal Decisions
Tutorial 8: Constrained Optimisation Optimality
Conditions
Exercise 1. Write down the optimality conditions for the following problem.
min f (x)
Ax b
Gx c
(0.1)
a x bb
Where f is a convex function, A is an m1 n matrix
Dynamical Systems and Deep LearningExercises 1 (solutions)
1. Find the dominant term and the smallest big O complexity of the following
expressions as x :
98x log x 23x1.1 .
Solution: 23x1.1 is dominant. O(x1.1 )
7x2
4x3
.
log x
3
3
4x
x
Solution: log
Dynamical Systems and Deep LearningExercises 2 (solutions)
1. Suppose we only have two neurons in the Hopfield network. Assume we have
(i) w12 = w21 = 1 or (ii) w12 = w21 = 1.
In the case of asynchronous updating, show that for (i) there are two attractin
C477: Computing for Optimal Decisions
Tutorial: The Newton-Raphson and Related
Methods
Answer 1.
a. We have f 0 (x) = 4(x x0 )3 and f 00 (x) = 12(x x0 )2 . Hence Newtons method can
be represents as,
xk x0
xk+1 = xk
3
Therefore,
2
xk+1 x0 = (xk x0 ).
3
b.
CO316 Computer Vision
Lecture 11 Image Sequence
Processing (Part 1)
Prof Guang-Zhong Yang
[email protected]
Su-Lin Lee, PhD
[email protected]
The Hamlyn Centre
for Robotic Surgery
Contents
Feature Detection
Interest Points in Vision
Corner D