[Insight-users] increasing bspline control point density

Miller, James V (Research) millerjv at crd.ge.com
Tue Jul 27 10:33:56 EDT 2004


The B-spline books that I use are:

Farin's books on NURBS and Computer Aided Geometric Design.  I tend to go
back to Farin since my first exposure to parametric curves was Farin's
books.  These books have a slant towards geometric design rather than
mathematical approximation.  So you might want a book on approximation
theory with B-splines.

Bartels, Beatty, Barsky book on splines for graphics and modelling. I
haven't gotten too deep into this book.  I got his book to help me make the
leap from splines for modeling to splines for approximation. Jury is still
out as to
whether it helps or not.

Nurbs: From Projective Geometry to Practical Use by Gerald E. Farin.
http://www.amazon.com/exec/obidos/tg/detail/-/1568810849/qid=1090938236/sr=8
-2/ref=sr_8_xs_ap_i2_xgl14/002-6657199-3627203?v=glance&s=books&n=507846

Curves and Surfaces for CAGD: A Practical Guide by Gerald E. Farin.
http://www.amazon.com/exec/obidos/tg/detail/-/1558607374/ref=pd_sim_books_1/
002-6657199-3627203?v=glance&s=books

An Introduction to Splines for Use in Computer Graphics and Geometric
Modeling
by Richard H. Bartels, John C. Beatty, Brian A. Barsky.
http://www.amazon.com/exec/obidos/tg/detail/-/0934613273/qid=1090938393/sr=1
-4/ref=sr_1_4/002-6657199-3627203?v=glance&s=books


In geometric modeling, splines are "presented" from a control point and knot
sequence viewpoint. In approximation theory, splines are "presented" from
the viewpoint of the trace of the spline. Here, knot vectors are usually
prescribed
(uniform) and points on the spline drive the estimation of control points.





-----Original Message-----
From: Karl Baum [mailto:kgbaum at syr.edu]
Sent: Saturday, July 24, 2004 11:39 AM
To: 'Miller, James V (Research)'; insight-users at itk.org
Subject: RE: [Insight-users] increasing bspline control point density


Jim,
 
Thanks for your help with this issue.

Could you recommend a good book on B-splines for me?

Karl
 

-----Original Message-----
From: Miller, James V (Research) [mailto:millerjv at crd.ge.com] 
Sent: Friday, July 23, 2004 8:47 AM
To: 'Karl Baum'; insight-users at itk.org
Subject: RE: [Insight-users] increasing bspline control point density

I do not think ITK provides a mechanism for increasing the number of 
control points in a B-spline grid.  However, the mathematics of B-splines
do support this operation.  There are formulas for adding a control point
to a B-spline that maintain the trace of the B-spline (shape of the
B-spline).

Any good book on B-splines will provide the formulas. 

Jim



-----Original Message-----
From: Karl Baum [mailto:kgbaum at syr.edu]
Sent: Thursday, July 22, 2004 5:22 PM
To: insight-users at itk.org
Subject: [Insight-users] increasing bspline control point density


Hi,
I am using BSplines to provide the transformations necessary for my
registration.  I would like to take an iterative approach where I first do
registration with a low control point density, and then use the results as
input to a registration with a higher control point density.  The issue I am
facing at this point in time is how to initialize the parameters of the
second iteration with the results of the first iteration.  In other words I
need to take the grid defined by the deformation coefficients of the first
iteration, and use it as input into the second.  To do this I need to
calculate the starting deformation coefficients on the higher density grid. 

Does itk provide anything to do this?  I was unable to find any
documentation addressing this.

Thanks,
Karl


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