IMGS 616 Fourier Methods for Imaging (RIT #11857)
Website: http://www.cis.rit.edu/class/simg716/ (note the URL)
The website will include links to lecture recordings and
scanned notes from each class. Note that this is an open website that does not
require a password – it is NOT part of the RIT “MyCourses” system, but may be
reached therefrom.
Instructor: Roger L. Easton, Jr., easton@cis.rit.edu,
Office 76-2112, Phone 1-585-475-5969, Office Hours TBD
and by appointment
Meeting Rooms/Times: Quarter 20131: TTh, 9:30am – 10:45am, Bldg. 76
(Carlson), Room 2155. Optional supplemental problem sessions may be scheduled.
NOTE: Foods and drinks/liquids are NOT allowed in the classroom – food
because of the “mess” factor, liquids because of the electrical outlets on the
tabletops – you may leave any such items on the table outside of the door
Also, turn off and put away any cellphones/PDAs during class time –
your focus is on the material, not on texting
I will be presenting an invited talk at the ICDAR
conference in
Prerequisites:
A complete course in
undergraduate Calculus is expected, including exposure to complex numbers. Any
additional experience with matrix algebra, linear algebra and complex analysis should
be very helpful.
Details: Homework will be assigned, and is to be
handed in on time (extensions will be considered in advance, though
cases of unforeseeable emergency will always be considered). Scores for
assignments handed in late will be penalized heavily and homework will not be
accepted after solutions have been posted. Problems (or some subset thereof)
will be graded and solutions to all problems will be handed out as quickly as
possible after the homework due date.
Homework – 30% (Assignments usually given Tuesday,
usually due 1 week later at start of
class).
Midterm Exams (closed book, closed notes, 75
minutes, anticipated dates: Tu 24 Sept.r and Th 31 Oct.) – 20% each
Final Exam (cumulative, closed book,
closed notes, 3 hours, Tuesday 17 December, 8AM-11AM, 76-2155) – 30%
This is challenging material for most
students (and is supposed to be). Despite (or perhaps because of) its demanding
nature, Fourier or linear systems theory must be mastered (not just
“understood”) for research in any area of imaging, which now is part of most
(if not all) disciplines of science. Fourier transforms appear in many (if not
all) areas of imaging as a means to describe and/or predict the action of
optical imaging systems and to filter digital or analog images. Though it is
possible to find disagreement from uninformed parties, it is very useful for
you to learn the principles of the continuous case to ensure understanding of
the discrete case.
Since this is a course that applies
mathematical tools to imaging situations, it is necessary to consider how to
implement the applications. In part, this will require the student to be able
to convert verbal descriptions into and solve the corresponding equations. For
many students, this task seems to be challenging and therefore requires some
practice. You can expect to be faced with such “word problems” during this
course.
You should expect to devote a significant amount of
time to this course outside of class. Even if you have some preparation in the
field (as from a linear systems course in electrical engineering), expect that
the different emphasis in this class likely will mean that you will have to
spend significant outside time to master the material. A rule of thumb for this
class is that you will spend 2-3 hours outside of class per hour in class,
which means that you should plan to spend 8-12 hours per week outside of
class. This time includes reading the text and related books besides doing
homework. Even if you finish the homework “early,” you should use any “extra”
time for additional reading on the subject throughout the term.
In the past, I have
generally scheduled supplemental and optional
“problem sessions” each week during the term (often Fridays at 4PM) for
students to ask questions and work on problems. These have generally been well
received by students. The Friday schedule may not be possible on a regular
basis this quarter due to family issues, so it may be necessary to investigate
other options (perhaps late afternoons and early evenings on Tuesdays). Again,
I emphasize that these sessions are optional.
This is our first experience
with the new RIT semester system. The way the schedule has been implemented, we
now have significantly less time to cover yet more material, so it will be even
more of a challenge to keep up. If you are having problems learning the
material, DON’T WAIT; ASK
EARLY for help – in and/or outside of class. Though I keep my
office door closed, PLEASE knock; if I am not doing something
urgent, I will set aside time to help – working with students individually or
in small groups is the most enjoyable part of my job. I am often in the office
on weekends, and spending some time to help students often is a nice break in
those days.
My philosophy on exams is
that they test understanding of material, which is the ability to
assimilate concepts and synthesize useful results in applications. This is not
the same as the ability to parrot discussions of concepts or replicate the
solutions to homework problems. In other words, you need to know how to apply
the material in the course. Be forewarned, my exams seem to have a reputation
among students, and I make no apologies, since this is a graduate program and
students must demonstrate mastery (not just “understanding”) of the material.
One issue that occasionally
crops up due to the different cultural backgrounds of students is the
appropriateness of working together. I encourage you to consult with your peers
on homework problems, though your submission must be your own work. For
example, if you are assigned work that requires submission of computer output,
you may consult with colleagues about programming questions, but you must
submit output from your own program and may not copy output from someone else.
On examinations, all work must be your own from start to finish.
Grading:
I
reserve the right for some flexibility, but the approximate mapping of numerical to
letter grades likely will be:
Note that the decision points for the bins are a bit
wider for higher scores and that the actual mapping may differ. Be advised that
scores at the margins tend to be placed in the lower grade. You likely are
already aware that students with fellowships must maintain an average of “B” or
better (GPA 3.0+) to continue their financial support and that ALL graduate
students must have this GPA or better to be in good standing for graduation –
all the more reason to deal with difficulties early rather than late.
All of that being said, I would give one (additional)
word of warning: one pet peeve of mine is the student who asks no questions in
class or out until immediately before some deadline (exam or due date for homework),
at which time questions are suddenly urgent. My advice is to ask
questions in sufficient time to have a positive impact on your understanding.
This
course may have a teaching assistant for grading, so I hope that the time
interval between submission and return of homework will be one week or less. I do
recommend that you keep a copy of your homework, as by scanning it to PDF before
submitting it. You may submit the PDF copies (in color if necessary) and retain
your original.
Course
Material:
This course introduces mathematical formalisms for
describing imaging systems, with emphasis on systems with responses constrained
to be linear in dynamic range and independent of spatial location in the scene.
In other words, the course develops mathematical models of imaging systems and
applies them to problems relevant to imaging.
Text
Materials:
Text: Fourier Methods in Imaging, R.L. Easton,
Jr., Wiley, 2010, ISBN 978-0-470-68983-7, list price $165 from Wiley (http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470660112.html, Adobe e-book format for $140). The book is available from
the usual suspects: the RIT Bookstore (B&N@RIT, http://rit.bncollege.com/), from Barnes and Noble as a printed book or in “Nook”
format for ~$97, and from Amazon.com as printed book or in “Kindle” format for ~$130. It is
available from the Society for Imaging Science and Technology at a substantial
discount of $120 including shipping (http://www.imaging.org/ist/store/physpub.cfm?seriesid=34&pubid=944)
The book considers continuous and discrete
imaging systems and optical imaging, and thus is relevant to the subsequent
courses IMGS-633 Optics for Imaging and IMGS-682 Digital Image Processing. Note there
is a long list of other books that touch on aspects of mathematical models of
imaging systems. You should peruse these and (at least) be aware of the
treatments (see the bibliography list). Though my book may be considered to be expensive
at $165 list, it is cheaper than many alternatives listed below and is useful
for at least two additional courses. In past years, some students have been
caught using electronic copies of the text that were downloaded from foreign websites.
Note that this is illegal under
Other useful books include:
1
Foundations of
Image Science, H.H. Barrett and K.D.
Myers, Wiley-Interscience, 2004, ISBN 978-0471153009 ($230 list, $161.48 from
Amazon.com) Catalog number TK8315 .B37 2004.
2
Linear
Systems, Fourier Transforms, and Optics,
Jack D.Gaskill, Wiley, 1978, ISBN 978-0471292883 ($225.00 list – good metric
for inflation index, as I bought it for $30 in 1980), QC355.2.G37: This formerly
was the text for this class and provides the inspiration for some homework problems.
3
Fourier
Analysis and Imaging, R.N. Bracewell,
Prentice-Hall, 2004, ISBN 978-0306481871. ($209.00 list) An earlier version, Two-Dimensional
Imaging, is in the RIT Library at call number TA1637.B73.
The book by Barrett and Myers (my research advisor and
a colleague from graduate school, respectively) considers much of the same material
up through optical imaging, though at a (much) more theoretical level and
without figures. I took Jack Gaskill’s class and used his book for many years.
It is still an excellent reference, though with the shortcoming that it does
not explicitly consider the discrete case.
Other books and resources are listed in the
bibliography: http://www.cis.rit.edu/class/simg716/Bibliography_616-20131.pdf
Obviously much material on the subject is available on
the internet, but I very seriously doubt that anyone can master Fourier methods
without becoming familiar (and spending time) with the standard texts. I
STRONGLY advise that you locate the shelves in the library where this material
is concentrated (Library of Congress call numbers beginning with TA,
One electronic resource you might consult are the
course lectures by Brad Osgood for EE261 at
Signals Software:
For demonstrations in lectures, I shall
often use my (ancient, but still serviceable) program “SIGNALS”
for PCs (which was written before some of you were born!). It is keystroke
driven from menus, so it is typically much faster to use in class than other available
software tools, such as MatLab. It may be downloaded from the CIS website:
http://www.cis.rit.edu/people/faculty/easton/signals/signals.zip.
An old (but still relevant) “user manual”
is available at: http://www.cis.rit.edu/resources/software/sig_manual/index.html.
The program was written to run in DOS (the
old PC operating system) and therefore cannot be used directly on “modern”
operating systems (after Windows 98). Fortunately, a free DOS emulator – DOSBox (available at http://www.dosbox.com/) allows the program to
run (and quite well) on a wide range of computer platforms including all
flavors of Windows (95, 98, XP,
Any version of DOSBox may be optimized for “Signals” by
editing the configuration file (see instructions on the DOSBox website or go to “Start à Programs à DOSBox à
Configuration à Edit Configuration” in Windows; then go to
the bottom of the file to the section labeled [autoexec] and insert the lines
listed below after “Lines in this section will be run at startup:”
#Lines in this section will be run at
startup
mount c (insert location of root directory for
Signals here, e.g., “mount c c:\2d”)
c: (switches to the drive letter defined in the previous
“mount” command)
cycles=30000 (you may want to experiment with this value
– faster computers can make use of larger numbers to speed up processing)
signals /c (starts the program with the “color”
display switch)
SignalShow:
A Java counterpart of Signals,
called SignalShow, was written as an undergraduate senior project
by Juliet Bernstein a few years back. SignalShow
goes beyond the original program in several ways, including illustration of the
2-D case, but it is neither completely free from bugs nor as fast for
experienced users. The beta releases of SignalShow for the three primary
computing platforms (Windows, Macintosh OSX, and Linux) are available at http://sourceforge.net/projects/signalshow/. A video introduction is available at http://www.youtube.com/watch?v=yDNipwKTMXM.
You may find this program very helpful in your quest
to visualize the concepts in this course, as well as in “Digital Imaging Processing,”
and in “Optics for Imaging.”
Other Software Tools
There
are plenty of other software available that may be helpful in this course:
·
ImageJ is a
freely available open-source program Windows, Linux and Mac OS X that has
evolved from former versions NIHImage
and ScionImage. Written in Java, the
basic program and “plugins” for more advanced routines are available from the
website http://rsbweb.nih.gov/ij/. Plugins are available for advanced processing
relevant to this and subsequent courses, including the Radon transform and
statistical analysis.
·
IDL / ENVI are
available on many computers in the
·
Matlab is
available from RIT for faculty and staff at reduced cost, but this offer does NOT
extend to students (don’t ask me why, because I don’t know)
Online Students: You MUST have a document scanner and software for converting the
scanned files to PDF (such as Adobe Acrobat with full features – not the free Acrobat Reader). You
should e-mail the PDF file of your homework to me; do NOT use FAX (the image
quality of faxed pages is often very poor and delivery of documents sent to the
department FAX machine cannot be guaranteed). Send the e-mail directly to me
rather than using the RIT “MyCourses” program to submit homework. MAKE SURE
that your submissions are readable before e-mailing them to me by reading over
the scanned files. The plan is to transmit lecture material live and
simultaneously with the onsite class and the lectures will be recorded for
later viewing. Recognize that technological failures of transmission and
recording are seemingly inevitable and should be anticipated. Since I will have
no assistant to monitor the system during lectures, it likely will not be
possible to respond to online questions in real time. I expect that online
students will find it more useful to ask questions offline before or after the
class during scheduled office hours or at some prearranged time. If you call
without an appointment, I pledge to respond at that moment if at all possible
unless I am engaged in something “urgent.”
20 August 2013