Biomedical Image Analysis Recipes in MATLAB: For Life Scientists and Engineers

421 Pages·2015·18.05 MB·English

by  Constantino Carlos Reyes-Aldasoro

Biomedical Image
Analysis Recipes
in MATLAB®
For Life Scientists and Engineers
Constantino Carlos Reyes-Aldasoro
LecturerinBiomedicalImageAnalysis
SchoolofMathematics,ComputerScienceandEngineering
CityUniversityLondon
London
Contents
1 The Basic Ingredients, 1
1.1 The Matlab Environment, 1
1.2 Introduction to Matlab, 3
1.3 Operations with Matrices, 7
1.4 Combining Matrices, 10
1.5 Addressing a Matrix, 13
1.6 Mathematical Functions and Graphical Display, 17
1.7 Random Numbers, 23
1.8 Statistics in Matlab, 26
1.9 Displaying Two-Dimensional Matrices, 29
1.10Scripts, Functions and Shortcuts, 37
1.11Using Help, 43
2 Introduction to Images, 45
2.1 An Image as a Matrix, 45
2.2 Reading Images, 46
2.3 Displaying Images, 49
2.4 Colormap, 54
2.5 Thresholding and Manipulating Values of Images, 59
2.6 Converting Images into Doubles, 68
2.7 Save Your Code and Data, 69
3 Introduction to Colour, 71
3.1 Mixing and Displaying Colours, 71
4 Western Blots, 79
4.1 Recipe 1: Many Ways to Display a Western Blot, 80
4.2 Recipe 2: Investigating the Numbers That Make a Western Blot, 93
4.3 Recipe 3: Image Histograms, 97
4.4 Recipe 4: Transforming an Image of a Western Blot, 104
4.5 Recipe 5: Quantification of the Data, 111
4.6 Recipe 6: Investigating Position of Bands, 121
5 Scratch Wound Assays, 135
5.1 Analysis of Scratch Wound Assays, 135
5.2 Recipe1:LowPassFilteringScratchWoundAssaysintheSpatialDomain,139
5.3 Recipe2:HighPassFilteringScratchWoundAssaysintheSpatialDomain,143
5.4 Recipe 3: Combining Filters and Morphological Operations, 154
5.5 Recipe 4: Sensitivy to Thresholds and Hysteresis Thresholding, 161
5.6 Recipe 5: Morphological Operators, 167
5.7 Recipe 6: Measuring Distances Between Cellular Boundaries, 178
5.8 Recipe 7: Introduction to Fourier Analysis, 187
5.9 Recipe 8: Filtering Scratch Wound Assays in the Fourier Domain, 201
References, 213
6 Bright Field Microscopy, 215
6.1 Recipe 1: Changing the Brightness and Contrast of an Image, 215
6.2 Recipe 2: Shading Correction: Estimation of Shading Component as a
Plane, 224
6.3 Recipe 3: Estimation of Shading Component with Filters, Morphological
Operators and Envelopes, 235
6.4 Recipe 4: Mosaicking and Stitching, 247
6.5 Recipe 5: Pixel Intensity and Histograms in Immunohistochemistry, 261
6.6 Recipe 6: Hue-Saturation-Value, 271
6.7 Recipe 7: Multidimensional Histograms, 278
Reference, 289
7 Fluorescence Microscopy, 291
7.1 Recipe 1: Separating and Combining Colour Channels, 294
7.2 Recipe 2: Investigating the Scaling of Values, 298
7.3 Recipe 3: Automatic Threshold Selection, 301
7.4 Recipe 4: Measuring Absolute and Relative Areas, 304
7.5 Recipe 5: Counting Nuclei, 305
7.6 Recipe 6: Quantification of Region Properties Beyond the Area, 308
7.7 Recipe 7: Dividing an Image into Regions, 310
7.8 Recipe 8: Batch Processing and Montages, 316
7.9 Recipe 9: A Myriad of Measurements, 327
References, 341
8 Creating Publication-Quality Figures from Matlab, 343
8.1 Recipe 1: Modifying the Characteristics of the Figures, 344
8.2 Recipe 2: Numerous Plots in One Figure, 352
8.3 Recipe 3: Three-Dimensional Ribbons with Different Annotations, 362
8.4 Recipe 4: Three-Dimensional Graphics, 378
8.5 Recipe 5: Projections, 388
8.6 Recipe 6: Four-Dimensional Data Set Explored, 391
Index, 401
Preface
Most newcomers to the emerging interdisciplinary fields inspired by biological prob-
lems, Systems Biology, Bioinformatics or Computational Biology, will face two difficulties.
The first is, of course, that in order to interact properly, a common understanding
of the “other” discipline is required. Engineers or computer scientists will need to
understand immunohistochemistry or molecular processes at a deep level; deeper
perhaps than the statistics and physics that biologists might need to understand. The
second problem, which is a bit more subtle, arises at conferences or meetings when
two collaborators on the opposite sides of the spectrum engage in a conversation
and after some time they begin to wonder if they are speaking the same language.
Suddenly, simple concepts do not appear to resonate in the same frequency for the
in-vivoscientistasforthemathematician.Sowhenyousay’model’areyoureallyreferring
to a mouse? Equally surprised may be the neurosurgeons when they listen to two
engineerstalkingaboutsomeNeuralNetworks,whichhaveverylittletodowithCajal’s
discoveries. A table at the end of this section shows a few words, which according to
the discipline, can have very distinct meanings.
Within this interdisciplinary atmosphere, the acquisition of images and more
generallysignalsofmanydimensionshasbecomeabridgebetweenfields:chemistry,
physics and engineering that develop new acquisition technologies, then biology
and medicine that apply the technologies to analyse specific problems and then
mathematics, computer science and statistics that try to extract meaningful infor-
mation of the signals. A systematic, algorithmic approach to the storage, processing,
classification and statistical analysis, the images can reveal much more than what
a human can observe. Furthermore, besides the technological advances that have
produced a myriad of imaging techniques, computers have decreased in price and
increasedinstoragecapacityandprocessingpower.Theneedforimageanalysisfrom
an algorithmic point of view is therefore essential to cope with the rate at which
the signals are produced, to provide more reliable and reproducible results and to
ease the labour to those who perform manual measurements for hours in front of a
microscope or a computer screen.
This book is designed as a tutorial for those researchers who are interested in
performingimageanalysisandwhosebackgroundisnotbasedonthestudyofapplied
mathematics. This book does not assume any previous knowledge of mathematics,
physics or programming except probably some basic principles with which most
life scientists should already be familiar. The basic concepts of image analysis are
presented without delving deep into the theory and applications, and solutions to
common biological images are presented. This is the emphasis of the book: to solve
common biological problems through the use of image analysis algorithms. In the
process of reading this book, a reader should then learn the basics of image analysis
and algorithm development so that he or she can then apply these new skills into
solving a particular problem in their own laboratories.
The book is based on Matlab, a mathematical language that allows a user to
execute flexible and powerful image analysis programmes tailored to the specific
needs of the problem. As the nature of Matlab is mathematical, there are numerous
textbooks designed for engineers and scientists who may already have a deeper
knowledge of mathematics and programming and other concepts such as linear
algebra and signals and systems. These books rarely delve into biomedical-specific
topics.
Thisbookisdesignedasarecipebook,inthesensethateachchapterwillpresent
one self-contained biomedical experiment to be analysed. Chapters 1–3 presents the
two basic ingredients of the book: essential concepts of image analysis and Matlab.
In Chapters 4–7, algorithm and techniques will be presented as a series of “recipes”
or solved examples that show the reader how a particular technique is applied in
a specific biomedical experiment. Four biomedical cases are analysed: Western Blots,
Scratch Wound Assays, Bright Field Microscopy and Fluorescent Microscopy. Each chapter
begins with simpler techniques, which then advance in complexity towards the
last recipes. Chapter 8 presents some advanced techniques for the generation of
publication-quality figures.
Therecipesaredesignedtoperformaspecificanalysisandlearnsometechniques
andalgorithms.Itisexpectedthatreaderswillbeabletoapplythesetechniqueslater
totheirownproblems.Inaddition,theywillhavethebasestoexploreMatlabfurther.
Term Context
Biological Nonbiological
Matrix Thewomb;theuterusofamammal. Arectangulararrayofsymbolsormathematical
Anamorphousorfibrillarmaterialthat expressionsarrangedinrowsandcolumns,
surroundscells;especiallytheextracellular treatedasasingleentity,andnowusually
substanceofconnectivetissue.Alsotheground writtenwithinroundbrackets.Alsogenerally
substanceinwhichstructuralelements(e.g.of anysimilartabulatedarrangementofitems.
ashell,cellwall,etc.)areembedded.
Vector Abacteriophagethattransfersgeneticmaterial Aquantityhavingdirectionaswellas
fromonebacteriumtoanother;also,aphage magnitude,oftendepictedbyalinedrawn
orplasmidusedtotransferextraneousDNA fromitsoriginaltoitsfinalposition.
intoacell. Anorderedsetoftwoormorenumbers
(interpretableasthecoordinatesofapoint);a
matrixwithoneroworonecolumn;also,any
elementofavectorspace.
Model Aperson,animalorplantthatcarriesa Asimplifiedoridealiseddescriptionor
pathogenicagentandactsasapotentialsource conceptionofaparticularsystem,situation,or
ofinfectionformembersofanotherspecies. process,ofteninmathematicalterms,thatis
Ananimalorplanttowhichanotherbearsa putforwardasabasisfortheoreticalor
mimeticresemblance. empiricalunderstanding,orforcalculations,
predictions,etc.
CHAPTER 1
The Basic Ingredients
1.1 The Matlab Environment
The word “Matlab” is an acronym for MATrix LABoratory. Matlab is a powerful
technical computing environment and a high-level computer programming lan-
guage, which provides core mathematics and advanced graphical tools for data
analysis, visualisation, as well as algorithm and application development. Matlab is
intuitive and easy to use, but it requires the use of command-line interface. That
is, contrary to other image-analysis software products, which have interfaces and
buttons, in Matlab the user needs to type commands to perform tasks. This may
seemdauntingforexperiencedusersofgraphical/textuserinterfaces.However,with
a little practice the command-line becomes easy to use. Furthermore, graphical user
interfacescanbecreatedwithinMatlab.Manycommonfunctions,algorithms,matrix
manipulationroutinesandplottingoptionsareavailableinthemainMatlabprogram
or on one of the many toolboxes that accompany Matlab.
ThereareseveralwaystostartMatlab:throughthe“MatlabIcon”ontheDesktop,
whichappearsontheDesktopofyourcomputerafterinstallationofMatlab,onMacs
itshouldbeunder“Applications>Matlab”andonWindowsin“Start>Programs”.The
following figure shows the location of the icons in a Mac Operating System.
BiomedicalImageAnalysisRecipesinMATLAB®:ForLifeScientistsandEngineers,FirstEdition.
ConstantinoCarlosReyes-Aldasoro.
©2015JohnWiley&Sons,Ltd.Published2015byJohnWiley&Sons,Ltd.
1
2 Chapter1
When you start Matlab, one or more windows will appear once the pro-
grammehasbeenlaunched.Thesemayincludethe'Desktop','Help Window',and
'm-file Editor', as shown in the following figure. You can later configure which
windows to launch with Matlab.
Themainwindowisthe'Desktop',whichissubdividedintoseveralsections.The
'Command Window'is where the instructions or commands are written to perform
a given task. The user will type the instructions in the 'Command Window'. For
example, we can add two numbers, 2 and 5, and store the result in the variable'a'
by typing the following in the'Command Window':
a = 2 + 5
a =
7
Toexecutecommands,theusermustpressthe“enter”or“return”keyaftertyping
each command. It is possible to have one or more commands in a single line, which
is sometimes called a line of instructions. After being executed, each line is stored in
the'Command History'window, together with the date when the command was
written. This can be very useful for repeating commands that were typed in the past
orforfindingthecommandsthatgeneratedacertainresult.TheCommandWindow
isthefirstplacewherecommandsareused,butifacomplextaskisneeded,itmaybe
better to store the commands in a file called an'm-file', which can be saved, edited
and debugged.
The 'm-files' are files of Matlab code that can be used as 'scripts' or
'functions'. Scripts are files in which a series of commands are written. When
the file is'run', all the commands will be executed in the sequence in which they
TheBasicIngredients 3
have been written. Functions are different; when a script is executed, any variable
thatexistsalreadyinMatlabmaybeused.Functionshavenoknowledgeofanything
thatexistsoutsidethefunction.Inorderforafunctiontoknowacertainvalue(stored
in a variable), this variable has to be “passed” to the function as input values or
'arguments'. In the same way, any variables that are created inside a script remain
in the'workspace'after the script is executed. With functions the opposite is true;
all intermediate variables created inside a function are deleted once the function
finishes its execution unless we specifically'pass'out the variable as an output
argument.
To edit the scripts or functions, Matlab provides an'm-file editor', which is a
specialtexteditorthatunderstandsMatlab;ithighlightsthecodeindifferentcolours
so that it is easier to read, it highlights possible errors in the code and suggests
improvements and it is very powerful to debug large functions. It even allows the
creation of documents. This entire book has been written in the Matlab Editor.
When the commands assign values to variables, a list of variables is displayed
on the'workspace'. Some characteristics of the variables such as their dimensions,
value, class ('double','single','char','cell', etc.) are shown. To visualise the
details of the variable or to modify some of the contents, a double-click on the
variablewilldisplayitonthe'Array Editor'.The'Help Window'providesdetailed
information about Matlab, functions, editors and toolboxes. New windows can
be used, for example when graphics are displayed as will be shown in the next
section.
1.2 Introduction to Matlab
In MATLAB everything is a matrix. A matrix should be understood in the math-
ematical sense as defined by the Oxford English Dictionary: “A rectangular array
of symbols or mathematical expressions arranged in rows and columns, treated as
a single entity, and now usually written within round brackets” and not as any
of the other definitions such as “the uterus of a mammal” or “the amorphous or
fibrillar material that surrounds cells”. Table 1 in the preface shows some terms with
extremely different meanings within the context of the Life Sciences and that of
Mathematics and Engineering. Therefore, a single number can be understood as a
matrix of dimensions 1×1, i.e. one row and one column. A pair of numbers can
be understood as a matrix of dimensions 2×1 or 1×2. This notion of “matrix
orientation” (horizontal or vertical) is a very important concept and will be very
relevant once operations are performed. Four numbers can be the elements of
matrices with dimensions 4×1, 1×4 or 2×2. It is not possible to leave “empty”
spacesinsideamatrix.Forexampleitwouldnotbepossibletoplacethreeofthefour
elements in the first row and the remaining element in the second row. That matrix
would automatically become a 2×3 matrix, that is two rows, three columns. The
“empty” spaces in the second row would be filled with zeros.
The values of a matrix, that is, the matrix itself, can be assigned to a “variable”,
which will store the values. The variable can be understood as the name by which
the matrix will be known. The basic objective of saving matrices as variables is that
they can later be used in conjunction with other variables. For example, to store the
valueof5inamatrixwiththename'a',thefollowingcodeistypedintheCommand
Window after the prompt (>>):
4 Chapter1
a=5
a =
5
After pressing enter, the value is stored, the workspace will show an entry for
'a'and Matlab will “echo” the answer to the command entered in the Command
Window.Inthiscase,theechojustrepeatswhatwastypedbefore,butitcanbeused
to find the solution of an equation with more data. For instance:
b = 45 + 123 + a
b =
173
Notice that we used the matrix'a'as one of the values to be added and stored in
the variable'b'. In this way, Matlab can be used as a simple calculator. If we are not
interested in saving the result, there is no need to assign it to a variable. Matlab will
store it in a temporary variable called'ans'(short of answer).
The order of precedence in which the operations are carried out is the following:
exponentiation,multiplication/divisionandthenadditionandsubtraction.Thisorder
can be modified by using round brackets. The order is sometimes referred to
with the acronyms “BODMAS” or “BIDMAS”, which stand for “Brackets, Order
of, Division, Multiplication, Addition, Subtraction” and “Brackets, Indices (powers
androots),Division,Multiplication,Addition,Subtraction”.Therefore,thefollowing
instruction line:
1 + 2 * 3 ˆ 4
ans =
163
is equivalent to:
1 + (2 * (3 ˆ 4))
ans =
163