Computers in Medicine Bone visualization and analyses - An introduction to Matlab - Presented by:...

Computers in Medicine

Bone visualization and analyses - An introduction to Matlab -

Presented by: Kathryn Stok

ETH Zurich

kas@ethz.ch

Prepared by: Steven Boyd

University of Calgary

Objectives (I)

Provide an overview of Matlab– What is Matlab?– Basic commands– Accessing online help– Writing M-files– Programming style– Create plots

Objectives (II)

Work through examples– Reading an image file– Probe the data– Filtering– Create a histogram– Thresholding– Counting voxels– Calculating 2nd moment of area

Why bone visualization?

Carries the body→ it should be strong

But in many cases, bone strength is impaired.– congenital deformities– osteoporosis– fracture– fatigue (stress fracture)

Bone architecture

Bone structure – femoral head

Young Normal Osteoporotic

Bone structure – lumbar spine

Young Normal Osteoporotic

Why bone visualization?

Bone (structure) analyses and visualization are of great importance in – Diagnosis– Treatment– Prevention

Why Matlab?

High-performance language for technical computing.– Matrix Laboratory

Advantages– Easy to use:

– No dimensioning required.– No compiling– Good for prototyping, testing

– Functionality is greatly expanded by toolboxes. – Many fields of application.

Disadvantages:– Uses much memory (slow for large applications)– Not good for final software design

What is matlab?

Matlab language– matrix/array language– control flow (if, for, while)– functions

Working environment– workspace for computing, importing, and

exporting data– text editor for creating M-files

This Matlab course

It covers: • Using the development environment.• Syntax of the language. • Basic matrix operations. • Basic graphics features. • Writing Matlab scripts and functions (m-files)

It does not cover: • Any of the toolboxes including Simulink. • c-mex and f-mex files, Matlab compilers.

Possibilities…

Develop tools for:– Image processing and basic analysis.– Visualization: 2D and 3D.– Simulation: Simulate bone loss.

Matlab Environment

Matrices

Albrecht Dürer

Magic square

Matrices

semicolon

Entering matrices– explicitly

Matrices

Sum, transpose

Matrices

Diagonal (diag)

Matrices

Subscripts: A(i,j)

row column

Matrices

Colon operator ' : '

Matrices

Colon operator ' : '

Matlab is 1-based

Matrix multiplication ( * )

Matrix multiplication ( .* )

Variables

Scalar, vector, matrix

Variables

Check workspace– command line– window

Numbers

Integer

Real

Exponential

Imaginary

-3

0.0001

1.60210e-20

5 + 2i

Operators: Arithmetic

+ Addition - Subtraction * Multiplication (or .* element-wise) / Division ^ Power (or .^ element-wise) ' Transpose () Brackets for evaluation order

A = [ 4 1 3]A.^2 = [16 1 9]A.*2 = [ 8 2 6]

A '* A 16 4 124 1 312 3 9

Operators: Relational

< Less than

<= Less than or equal to

> Greater than

>= Greater than or equal to

== Equal to

~= Not equal to

Operators: Logical

& AND

| OR

~ NOT

Type help ops to see: the arithmetic,relational and logical functions.

Matrices

Entering matrices– explicitly– load from external file– your own M-files– built-in function

Albrecht Dürer

Generating matrices

Loaddata file

Generating matrices

M-files

Generating matrices

Built-in functions

Help

Help Window– pop-up window

Type help

Online help

Online help

Online help

Useful commands

(up arrow)– recall previous command– p recalls previous command starting with ‘p’

clear– clear workspace– clear A Z Q clears only A, Z, and Q.

size– size(A) returns size of matrix A

Multidimensional matrices

page k,Z

rowi, X

column j, Y

Multidimensional matrices

Generate a 3D array manually

Advanced indexing

Matrices are always stored as columns– subscripts (i,j,k)– array dimension [d1 d2 d3]

– if A is of dimension 3 x 3 x 3 then A(3,3,3) = A(27) = 8

3 2 7 5 1 1 4 6 8 6 2 6 1 4 9 3 6 7 5 6 7 9 5 6 1 2 8

3 5 4 2 1 6 7 1 8

3 5 4 2 1 6 7 1 8

6 1 3 2 4 6 6 9 7

6 1 3 2 4 6 6 9 7

5 9 1 6 5 2 7 6 8

5 9 1 6 5 2 7 6 8

ij

k

Characters and Text

s = 'myimage'– 7 character array (string)

num2str() - convert a number to string

User input

Keyboard inputa_number = input('Enter number');a_string = input('Enter filename', 's');

[filename,path] = uigetfile('*.*');

Using GUI

Graphics: plot

Graphics: plot(s)

‘hold on’allows more plots to be added

Graphics: contours

Graphics: subplots

Graphics: labels and titles

Graphics: labels and titles

… or use the Figure window !

Graphics: mesh

Flow control

if, else, and elseif

switch

while

for

if, else, and elseif

if logical_expression statementsend

if (rem(a,2) == 0) disp(‘a is even’)end

if (n<0) disp(‘Input must be positive’)elseif (rem(n,2) == 0) disp(‘a is even’)else disp(‘a is odd’)end

switch

switch expression case value1 statements case value2 statements otherwise statementsend

switch (input_num) case (-1) disp(‘negative one’) case (0) disp(‘zero’) case (1) disp(‘positive one’) otherwise disp(‘othervalue’)end

while, for

while expression statementsend

n = 1;while (prod(1:n) < 1e10) n = n + 1;end

for index = start:inc:end statementsend

for i = 2:6 x(i) = 2*x(i-1);end

for i = 1:m for j = 1:n A(i,j) = 1/(i + j - 1); endend

Vectorization

Efficiency!– Example: Table of logarithms

–Find log10 of numbers between 0 and 10.

x = 0;for k = 1:1001 y(k) = log10(x); x = x + 0.01;end

x = 0:0.01:10;y = log10(x);

Looped code Vectorized code

AVOID LOOPS!

Scripts and functions

Scripts– No input arguments nor

output arguments.

– Operate on data in the workspace

– Useful for automating a series of steps that will be performed many times

Functions– Can accept input

arguments and return output arguments

– Variables are local to the function

– Useful for extending the MATLAB language beyond the built-in functions

Script example

Comment lines

Computations

Graphicsoutput

Create m-files:– type edit – use the interface

Script example

Hit return to advance plot

Script Example

Function example

Function definition

Help comments

Error check

Calculations

function [y] = average(x)

keyword

output argumentfunction name

input argument

Function example

semi-colon

M-files

Tips:– use descriptive variable names

–e.g. number_students = 20– functions end with “_fcn”

–e.g. an_example_fcn(number_students)– indent if, for, while statements 3-4 spaces– add comments using ‘%’– develop with smaller portions of data– debug by pasting line-by-line from M-file

Online tutorial

http://www.imrtweb.ethz.ch/matlab/

Or google “mathworks tutorial”

Fundamentals

Exercises

Examples

Part II: Practical Programming

Image analysis on 2D section– Read image data (micro-CT)– Plot the image– Examine image– Filter the image– Create a histogram– Threshold (distinguish between bone and marrow)

– Calculate porosity– Centroid, principal axes

Read 2D Image

Want to import the image from micro-CT

Write a program to:– clear workspace– set filename– load file

– Image data to visualize:/Phalanx/hp2d_34-95_380.bmp

Set up main program (a script file)

comments

clear workspace

close all figure windows

file to load

load it

Note: You need to write the 2D image reading function.

Read in 2D image

Read the file

Convert data

Display input data

Display input data

Display input data

Examine image

min, max, mean

Examine image

min, max, mean

Image Processing

Filter

Thresholding– histogram

Porosity = 1 - (bone area / total area)

Moment of area– First moment of area– Centroid– Second moment of area

Filtering – example 1

Filtering – example 2

filtered original image filtered noisy image

original image noisy image

Filtering the data

Apply Gaussian filtration– Shape of filter depends on:

window size [n1 n2] and

Filtering

Window = 3 = 1.2

Filter

Filtering

Window = 5 = 1.2

Filter

Filtering

Window = 15 = 1.2

Filter

Filtering

Window = 15 = 7

Filter

Filtering

Window = 15 = 100

Filter

Filtering: Convolution

zyx fff

Filtering: Edge Effects

edge data nulled

• Important to begin with image dimensions large enough to account for edge effects

Filtering

Use built-in functions:– fspecial– imfilter– (smooth3)

Thresholding

• Good to try different thresholds to see the effect.

Segmentation of bone– divides bone from other tissue

Thresholding

threshold2D = zeros matrixFind all indices (i,j) where element(i,j) > threshold threshold2D(i,j) = 1

Thresholding

Thresholding

Threshold = 90 Threshold = 120

Histogram

– lookfor and help

Histogram

hist works on vectors, not 2D matrices– need reshape function to vectorize

Porosity

Porosity = 1 - (Bone volume divided by total volume)

Need total bone volume (area)– Create mask:

– filter image to remove holes– threshold filtered image

– Count total “mask” pixels– Count total “bone” pixels

within mask

Porosity

Create mask:

original image

filtered image

threshold filtered image

Image 3 super-imposedon image 1

1 2 3

Porosity

Porosity = 1 -Mask pixels

Bone pixels within mask

Thresholded image (bone)

Mask image

Image of bone within the mask

Image analysis – determine porosity

Original

Segmenting the boneFiltered Thresholded

Creating the maskFiltered Thresholded

Find bone within mask

Porosity = 1 - Areabone

Areamask

Erosion, dilation

Erode Erode = 2 Erode = 4

Dilate Dilate = 2 Dilate = 4

Part of MAIN program

Stress in Pure Bending

Mechanical stiffness– First moment of area– Centroid of area– Second moment of area

First moment of an area

First moment of area with respect to the X axis:

First moment of area with respect to the Y axis:

Can be positive, negative, or zero depending on the axis location

(mm3)

(mm3)

Centroid of an area

Centroid of area defined as:

Knowing the first moment:

First moment of area

Second moment of area

Stress resulting from bending: σ = My/I

Resistance against bending.– Take Ix, Iy, Ixy about centroid C

– Or use the parallel axis theorem: Ix = Ixc + Ad2

Second moment of area - rotation

Transformation of 2nd moments:

Second moment of area - principal axes

Two values of for which Ixy = 0.

Can calculate the max/min 2nd moments:

maximum associatedwith Ix

minimum associatedwith Iy

Principal axes & Transformation

2D: Pompe Disease

Radius Tibia

Mouse knees

NTRTCTRL