Feature point extraction

There are two important requirements for feature points. First, points corresponding to the same scene points should be extracted consistently over the different views. If this were not the case, it would be impossible to find correspondences amongst them. Secondly, there should be enough information in the neighborhood of the points so that corresponding points can be automatically matched. Many feature point extractors have been proposed [120,59,52,31,180].

In our system the Harris corner detector [59] is used. Consider the following matrix

$${\bf M}=\left[ \begin{array}{cc} \left(\rule{0mm}{4mm}\frac{... ...4mm}\frac{\partial I}{\partial y}\right)^2 \end{array} \right]$$ (D1)

where $I(x,y)$ is the grey level intensity. If at a certain point the two eigenvalues of the matrix ${\bf M}$ are large, then a small motion in any direction will cause an important change of grey level. This indicates that the point is a corner. The corner response function is given by:

$$R= \det {\bf M} - k (\mbox{trace} {\bf M})^2$$ (D2)

where $k$ is a parameter set to 0.04 (a suggestion of Harris). Corners are defined as local maxima of the cornerness function. Sub-pixel precision is achieved through a quadratic approximation of the neighborhood of the local maxima.

To avoid corners due to image noise, it can be interesting to smooth the images with a Gaussian filter. This should however not be done on the input images, but on images containing the squared image derivatives (i.e. $\left(\rule{0mm}{4mm}\frac{\partial I}{\partial x}\right)^2, \left(\rule{0mm}{4... ... I}{\partial x}\right)\left(\rule{0mm}{4mm}\frac{\partial I}{\partial y}\right)$).

In practice often far too much corners are extracted. In this case it is often interesting to first restrict the numbers of corners before trying to match them. One possibility consists of only selecting the corners with a value $R$ above a certain threshold. This threshold can be tuned to yield the desired number of features. Since for some scenes most of the strongest corners are located in the same area, it can be interesting to refine this scheme further to ensure that in every part of the image a sufficient number of corners are found.

In figure 4.1 two images are shown with the extracted corners. Note that it is not possible to find the corresponding corner for each corner, but that for many of them it is.

Figure 4.1: Two images with extracted corners