Databases
StackOverflow2013
Postsdbo
PO
 

Note that there are some explanatory texts on larger screens.

plurals
  1. PO
    primarykey
    data
    text
    <p>I had to go back to the <a href="http://www.vision.ee.ethz.ch/~surf/eccv06.pdf" rel="nofollow">original paper</a> to find the precise answers to your questions.</p> <p><strong>Some background first</strong></p> <p>SURF leverages a common Image Analysis approach for regions-of-interest detection that is called blob detection. The typical approach for blob detection is a difference of Gaussians. There are several reasons for this, the first one being to mimic what happens in the visual cortex of the human brains.</p> <p>The drawback to difference of Gaussians (DoG) is the computation time that is too expensive to be applied to large image areas.</p> <p>In order to bypass this issue, SURF takes a simple approach. A DoG is simply the computation of two Gaussian averages (or equivalently, apply a Gaussian blur) followed by taking their difference. A quick-and-dirty approximation (not so dirty for small regions) is to approximate the Gaussian blur by a box blur.</p> <p>A box blur is the average value of all the images values in a given rectangle. It can be computed efficiently via <em>integral images</em>.</p> <p><strong>Using integral images</strong></p> <p>Inside an integral image, <em>each pixel value is the sum of all the pixels</em> that were <em>above</em> it and on its <em>left</em> in the original image. The top-left pixel value in the integral image is thus 0, and the bottom-rightmost pixel of the integral image has thus the sum of all the original pixels for value.</p> <p>Then, you just need to remark that the box blur is equal to the sum of all the pixels inside a given rectangle (not originating in the top-lefmost pixel of the image) and apply the following simple geometric reasoning.</p> <p>If you have a rectangle with corners ABCD (top left, top right, bottom left, bottom right), then the value of the box filter is given by:</p> <pre><code>boxFilter(ABCD) = A + D - B - C, </code></pre> <p>where A, B, C, D is a shortcut for IntegralImagePixelAt(A) (B, C, D respectively).</p> <p><strong>Integral images in SURF</strong></p> <p>SURF is not using box blurs of sizes 9x9, etc. directly. What it uses instead is several orders of Gaussian derivatives, or Haar-like features.</p> <p>Let's take an example. Suppose you are to compute the 9x9 filters output. This corresponds to a given sigma, hence a fixed scale/octave.</p> <p>The sigma being fixed, you center your 9x9 window on the pixel of interest. Then, you compute the output of the 2nd order Gaussian derivative in each direction (horizontal, vertical, diagonal). The Fig. 1 in the paper gives you an illustration of the vertical and diagonal filters.</p> <p><strong>The Hessian determinant</strong></p> <p>There is a factor to take into account the scale differences. Let's believe the paper that the determinant is equal to:</p> <pre><code>Det = DxxDyy - (0.9 * Dxy)^2. </code></pre> <p>Finally, the determinant is given by: <code>Det = DxxDyy - 0.81*Dxy^2</code>.</p>
    singulars
    1. This table or related slice is empty.
    1. POHow to apply box filter on integral image? (SURF)
      singulars
      1. PTQuestion
    1. PTAnswer
    1. USsansuiso
    1. USsansuiso
    plurals
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. COOK, I understand that, but there are 4 octaves with 4 filters. Call me stupid, but I still cannot see how to apply 9x9 filter for the first octave. How to calculate A, B, C and D? Or maybe A is a 9x9 square, B is 15x15 square, C is 21x21 square and D is 27x27 square?
      singulars
      1. PO
      1. USmoose
    2. COA pixel A of the integral image is the sum of all pixels of the original image from the top-left corner down to A. Therefore A + D - B - C is.... (draw yourself a picture to see what you get)
      singulars
      1. PO
      1. USFrancesco Callari
    3. CO@Francesco, I hear you, but such ABCD rectangle can be of any size placed anywhere within integral image. Does it mean that ABCD = 9x9 square? If it is, how to position that ABCD square over integral image in order to calculate A+D-B-C? In other words, vertex 'A' should be placed where?
      singulars
      1. PO
      1. USmoose
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload