<div>Hi, Andreas,</div>
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<div>Thanks for your reply. I thought the mentioned book was written in conjunction with the ITK consortium, so couldnt find a better place to clarify.</div>
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<div>Has anyone else noticed the same thing from itk-users? Is there a better way to report this than contacting authors directly?</div>
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<div>Thank you.</div>
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<div>[Pixel.to.life]</div>
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<div>>>>>>>>>>>>></div>
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<div>Date: Wed, 25 Apr 2007 10:07:15 +0200<br>From: "Andreas Keil" <<a onclick="return top.js.OpenExtLink(window,event,this)" href="mailto:andreas.keil@cs.tum.edu">andreas.keil@cs.tum.edu</a><span></span> >
<br>Subject: RE: [Insight-users] Q on Jacobian in "Insight into Images:<br> Principlesand Practice for Segmentation, Registration, and Image<br> Analysis"<br>To: <<a onclick="return top.js.OpenExtLink(window,event,this)" href="mailto:insight-users@itk.org">
insight-users@itk.org</a>><br>Message-ID: <002b01c78710$bcba4920$690a9f83@08keil><br>Content-Type: text/plain; charset="us-ascii"<br><br>Hi [Pixel.to.life],<br><br>I don't know the book but from your quote it's clear that you found a
<br>typo. The Jacobian is always the matrix of first derivatives of a<br>vector-valued function:<br><br> J_ij = d f_i / d x_j (where "d" indicates partial derivatives)<br><br>(In case of a scalar-valued function this would reduce to the gradient
<br>vector.)<br><br>And as you already said, the Hessian is the matrix of second derivatives<br>in case of scalar-valued functions:<br><br> H_ij = d^2 f / d x_i d x_j<br><br>(In the case of vector-valued functions this would get three-dimensional -
<br>a so-called tensor, I think.)<br><br>Therefore, I totally agree with you and you should report the typo if<br>possible.<br><br>Regards,<br>Andreas.<br><br><br>-----Original Message-----<br>From: insight-users-bounces+andreas.keil=
<a onclick="return top.js.OpenExtLink(window,event,this)" href="mailto:cs.tum.edu@itk.org">cs.tum.edu@itk.org</a><br>[mailto:<a onclick="return top.js.OpenExtLink(window,event,this)" href="mailto:insight-users-bounces+andreas.keil=cs.tum.edu@itk.org">
insight-users-bounces+andreas.keil=cs.tum.edu@itk.org</a>] On Behalf<br>Of Pixel Life<br>Sent: Wednesday, April 25, 2007 06:42<br>To: <a onclick="return top.js.OpenExtLink(window,event,this)" href="mailto:insight-users@itk.org">
insight-users@itk.org</a><br>Subject: [Insight-users] Q on Jacobian in "Insight into Images:<br><span></span>Principlesand Practice for Segmentation, Registration, and Image Analysis"<br><br>Hi,<br><br>I am looking for clarification on a topic published in the book "Insight
<br>into Images: Principles and Practice for Segmentation, Registration, and<br>Image Analysis". I use it in conjunction with itk examples. (if the<br>question is not relevant here, please advise).<br><br>>From page 31, page
2.4.8, I quote: : "...Where the first derivative<br>(gradient) is represented as a vector, the second derivative is a matrix,<br>known as the Jacobian.."<br><br>However, on page 249, Jacobian is presented as a matrix of first order
<br>partial derivatives.<br><br>Even in all the literature I can find, the term 'Jacobian' is used to<br>represent a matrix of first order partial derivatives. I did see 'Hessian'<br>as a representation of 2nd order partial derivatives in a matrix form.
<br><br>The question is: am I missing some information here (e.g. the<br>terminology?), or the book on page 31 has a typo?<br><br>Thank you for the help.<br><br>[Pixel.to.life]<br><br> </div>
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