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    Normalized correlation with a constant vector

    Yes, that is exactly what I am observing. You got it :)
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    Normalized correlation with a constant vector

    I am confused how to interpret the result of preforming a normalized correlation with a constant vector. Since you have to divide by the standard devation of both vectors (reference: http://en.wikipedia.org/wiki/Cross-correlation#Normalized_cross-correlation ) , if one of them is constant (say a...
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    Vector difference metric that considers the variance of the components

    @chiro - what kind of statistical techniques? Are you suggesting just computing a Euclidean style distance between local FFT components or something like that? Doesn't this ONLY contain frequency information, and no information in the spatial domain (i.e. the colors don't have to match at all)...
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    Vector difference metric that considers the variance of the components

    Yep, that's what I want :) Of course there isn't a perfect one, but I thought someone here might have an idea of a better one than a simple Euclidean distance. Assume everything is quite low resolution. For instance, this picture of the entire house/grass/road is ~500x500. Yes, only...
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    Vector difference metric that considers the variance of the components

    Hi Stephen, The values are just the RGB pixel values. It does very well in most cases, but when it fails (like the case I described), it fails miserably. Yes, simple and fast is definitely a requirement. I would like to avoid this at all costs :) I hope this clarifies some...
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    Vector difference metric that considers the variance of the components

    I am trying to match little square patches in an image. You can imagine that these patches have been "vectorized" in that the values are reordered consistently into a 1D array. At first glance, it seems reasonable to simply do a Euclidean distance style comparison of two of these arrays to get a...
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    Weighted least squares best fit plane

    I know that the plane through the center of mass whose normal is the eigenvector corresponding to the smallest eigenvalue of the scatter matrix of a set of points is the best fit plane. I now want to do a "weighted least squares" - would I simply multiply the...
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    Distance difference problem

    I think it works if you just use the law of cosines. See attached.
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    Distance difference problem

    Gah, you are right. However, this requires I have p. What if I don't have p?
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    Distance difference problem

    I guess another way to say it is: "I need a difference function which will produce 'x' for f(p,d1) and also produce 'x' for f(d2,d1)"
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    Distance difference problem

    I guess even better would be some transform of each distance, so that: f(d1)-f(p)=f(d2)-f(d1) of course f() may not be exactly the same function, it may depending on the position (i.e. it could be f(d1)-f(p)=g(d2)-g(d1) or something like that).
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    Distance difference problem

    See the image in the attached document. I am looking for a function which will make f(d1-p)=f(d2-d1)=f(d3-d2) (see the very last part of the document) I thought it would be as simple as dividing by the angle between the lines, but that doesn't seem to work. Is it reasonable to do this...
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    Why do we have to learn that?

    This is for mathematics students. Certainly if you study mathematics as your "field" then you should know these things. But engineers need not know them, and certainly people studying/practicing non-technical disciplines need not study them in high school.
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    Why do we have to learn that?

    Haha Manheis, as I was reading this thread I was thinking "how has no one posted the Worlfram TED talk??". I don't work for Wolfram either, but he is definitely right. Frankly, I am quite shocked that people here do not support this concept. The people who will build the next-gen Maple style...
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    Interpretation of power rule for integration applied to 1/x

    We all know \int \frac{1}{x} dx = ln(x) + c but if you try to apply the power rule for integration: \int x^n dx = \frac{x^{n+1}}{n+1} + c you get \int x^{-1} dx = \frac{x^0}{0} What can you learn from this/what does this mean? David
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    Wolfram answer for cubed root of -1

    So they are just giving the first solution? I'm confused why it doesn't say, -1, e^{i\pi / 3}, e^{-i\pi / 3} ?
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    Wolfram answer for cubed root of -1

    At http://www.wolframalpha.com/ , if you type: 1) (-1)^(1/3) It gives a complex approximation. Isn't it exactly -1? David
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    Volunteers for an Experimental Teaching Tool

    You're right - the software may be fine. What I'm claiming though is that there needs to be many people from many fields working together to effectively produce a teaching tool. Typically this is done by the "content expert" alone. He is typically not versed in the "art" of teaching, or...
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    Volunteers for an Experimental Teaching Tool

    I am starting a project to develop, with a very diverse team, an open source, modular, web-based teaching tool for math, science, and engineering courses. Here is a link to the full project description...
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    Developing Mathmatical Maturitiy

    It's not the students fault, it's poor explanations! Don't sweat it - try to gather as many resources as you can to try to take bits and pieces from them all until it makes sense (what the authors should have done before writing a book...) Dave
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    Differential Equations vs Linear Algebra

    What applications are you interested in? Some fields use linear algebra heavily (computer vision) and some field use differential equations heavily (control theory). Dave
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    Help solving an equation for 3d modeling

    I agree with Lorc Crc - I wouldn't do any "crossing out" in linear algebra - or even division for that matter - always move things around with the inverse operation. Dave
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    Fitting a quadric function to a set of points

    Zaphos, You have been very helpful, thanks! You are right on - I just thought it was an "error", but in fact it makes a lot of sense that the plane is the best fit to a set of sphere points. Do you have a recommendation of a similar non-height field type of fitting procedure? Thanks...
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    Fitting a quadric function to a set of points

    Where did you get a8 = -1 ? It seems to work with some point sets, but for others (points sampled from a sphere, for example) the result is wrong (it says all of the coefficients are 0). Is there a reason that would happen? Thanks, David
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    Fitting a quadric function to a set of points

    1) Hm... isn't it just the standard least squares solution, or Ax = b x = A^{-1}b or in this case since A is not invertible x = pinv(A) b where pinv is the pseudo inverse? 2) The second part - I was saying that in order to "see" this fit, I have a function in a toolbox that will plot...
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    Fitting a quadric function to a set of points

    I have a set of points and I want to find a "best fit quardric surface" through the points. I did the following: 1) Assume the function is in the form: a x^2 + b y^2 + c xy + d x + e y + f = z 2) Make a nx6 matrix of the points put into (1), that is A=: x1^2 y1^2 x1y1 x1 y1 1 x2^2 y2^2...
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    Prove that the lim as x goes to a of sqrtx = sqrta

    I think it would be very helpful if you guys used latex The question should be Proove that \lim {x \rightarrow a} \sqrt{x} = \sqrt{a} And the first reply should be start with \sqrt{x}-\sqrt{a}=\frac{x-a}{\sqrt{x}+\sqrt{a}} For basic things like this, latex only takes about a minute to...
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    How to get step-by-step integration

    What do you mean? Like you want to see the Riemann rectangles shrinking to 0 width?
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    Determinant of an orthogonal matrix

    Maybe you can share your new knowledge with the forum so that when other users see the question they can also see the answer!
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    Min cut on a graph

    Anyone?
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