For the purpose of defining an adaptative filter, Yang et al
[3] proposed a technique for defining and computing
a measure of anisotropism at each point within an image. In that paper,
the issue of corner identification has been addressed. Here we show
how it can be extended to corner orientation detection.
For a strongly orientated intensity pattern along one direction, the
power spectrum clusters along a line through the origin in the Fourier
domain. By determining this line, and how closely it approximates the
Fourier transform of the image, the orientation 
and the
strength g of the anisotropism of the pattern can be derived. It
has been demonstrated that the computation of g and
does not require the actual computation of the Fourier
transform. Indeed, the analytical expressions obtained are:
with the same notations as those used in Equation (1). In
Equations (2) and (3) 
is a small
neighbourhood of 
. This scheme uses single derivatives only,
which are integrated, and thus it reduces the effect of noise.
The value of 
is 1 for a strongly orientated pattern along
one direction, and is 0 for isotropic regions. For real images with a
low signal-to-noise ratio, this method proves to be more robust than
the mere estimation of the gradient direction.
In order to apply the above technique to corner recognition, we introduce two assumptions about the characteristic features of corners:
with 
being a monotonic decreasing function from 1 to 0
within [0:1]. In our implementation, we chose:
with m=2 typically. Figure 11 shows
an example of the computation of the fields required for estimating
cornerness. (a) is the original synthetic image. (b) shows the gradient
magnitude. (c) shows the anisotropism which is high along the edges
and low at corner points. (d) and (e) show cornerness with different
window settings. The orientation 
which is required
at a later stage of the algorithm, is also given, shown as (f).
Figure 1: a) Original image 
. b) Gradient magnitude 
. c) Anisotropism . Straight edges are strongly anisotropic along one direction whereas corner points are not. d) Cornerness 
. e) Cornerness with different window settings: precise corner pixels can be identified. f) Direction of anisotropism (on a gray-scale from 0 - black to 
- white). It gives the orientation of the edges, but cannot be used within the immediate neighbourhood of corners.
Extracting the actual corner points is achieved by analysing the
histogram of the cornerness image. A small proportion of pixels
( 
) with sufficiently high values can be regarded as
belonging to corners. Each cluster of such points is labelled as one
corner, at the position of its point of highest
cornerness. Experiments show that some simple edge points may be
misclassified as corners this way, especially if is chosen too
high and for noisy images. This, however, has little detrimental
effect on the algorithm, since at a later stage these pixels can be
easily identified and discarded.
