- ...output.
- Note that the scale on
the vertical axis is inverted.
- ...positives.
- Canny develops
Criterion 1 to mean that the edge enhancing filter should
maximize the signal-to-noise ratio. This makes sense in the case of a
linear filter which has features thresholded at a later stage than the
enhancement, and Canny formulates a signal-to-noise functional which
expresses this requirement. However, the SUSAN principle is
fundamentally non-linear. (This can be simplistically interpreted as
performing thresholding at an earlier stage.) In fact, it is clear
from Figure 4 that the term ``enhancement'' is a little
weak, given the obvious signal-to-noise ratio. (The plot of the
operator output shows no visible noise.) Thus the criterion is most
appropriate as it stands.
- ...model''
- This edge detector combines the outputs of two
filters to attempt to find both step edges and ridge/roof edges. It
basically performs a simple test to find maxima in the first or second
derivatives.
- ...edges
- Much research in this field has assumed that the only
one dimensional features of interest are step edges. However, there
exist many other types of feature. These include lines (ridges in the
image surface), ramp ends and roof edges; see
Figure 9 for examples of these. There are three main
reasons for the concentration on step edges. The first is that they
are the most common type of one dimensional change. The second is that
edges containing a step component are the most well localized one
dimensional features, that is, they are formed by a ``first order''
change. The third reason for working only with step edges is that some
proposed edge finders (such as Canny's) are easily extended to finding
other types of change once the theory for step edges has been
completed. Thus many detectors have been developed using rigorous
derivations of optimal algorithms using various criteria based on the
model of the ideal step edge.
- ...Gaussian.
- The problem with using image derivatives is that
differentiation enhances noise as well as edge structure, so most edge
detectors include a noise reduction stage. Thus the use of the
derivative of a Gaussian enables differentiation to take place at the
same time as the smoothing; this is allowable, as the two processes
commute (exactly in the continuous case, and approximately in the
discrete case). The problem of noise enhancement is even worse when
differentiation is performed twice.
- ...poor,
- Some higher level
algorithms use Canny's method because of this characteristic, as
they work better with simple unconnected edges. However, achieving
full connectivity at junctions is clearly a worthwhile goal as it
correctly represents the scene. In [32] Li et. al. suggest
heuristic extensions to the Canny algorithm to enable the joining of
open contour ends with nearby contours. This however produces some
false edge extensions.
- ...responses.
- In [9] the circular Gaussian mask is
developed into a non-circular one once edge direction has been found.
This reduces the contribution of noise to the edge signal. This step
could be mirrored in the SUSAN algorithm, but there is no need, as no
signal as such is being filtered, and the noise reduction is already
large due to integration over the mask.
- ...comparison.
- The software implementation uses a value of 100
rather than 1 for the maximum similarity, so that integer arithmetic
may be used rather than floating point, for speed of computation.
- ...threshold''
- Note that the only threshold introduced in
this paper which is not optimally established by careful
analysis is t, the brightness difference threshold. This is the
parameter which controls the sensitivity of the feature detection
algorithms. Feature detection applications almost always require that
sensitivity can be controlled by variation of one or more parameters,
preferably only one.
- ...designed.
- All images shown in this paper are
256 by 256 pixels in size, except in a few cases where small sections
of images have been used, or where otherwise stated. Where
appropriate, images have been scaled horizontally for display.
- ...ratio
- The minimum signal to
noise ratio is taken to mean the ratio of the smallest edge height to
the standard deviation of the added Gaussian noise.
- ...map.
- This result also shows the success of the SUSAN
edge detector when used for finding lines in the image.
- ...model
- Here model means the type of image
structure assumed to be present when discussing any particular aspect
of corner finding theory. Note that almost all approaches to corner
finding assume a simple corner model, whether or not they are
``model based''.
- ...algorithm.
- The Plessey
corner detector (also known as the Harris detector) should perhaps be
referred to as the (very closely related) Förstner detector, as
the latter appears in earlier literature. However, the Plessey
detector is more widely known and referenced, so for ease of
understanding the name Plessey is used here.
- ...detected.
- This assumes that the USAN is a
contiguous region. The refinements described later are designed to
enforce this contiguity.
- ...respectively.
- These images are only
128 by 128 in size.
- ...hardware
- Sometimes even
some structure in the imaged world is treated as unwanted ``noise''.
- ...image.
- This is
assuming digital storage and not analog.
- ...algorithm.
- The acronym is carried over from the closely
related SUSAN feature detection algorithms. For naming accuracy, the
acronym could now read Smoothing over Univalue Segment Assimilating
Nucleus.
- ...100.
- All
brightness values mentioned are within an image brightness scale of 0
to 255.
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