Note that the scale on the vertical axis is inverted.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

This result also shows the success of the SUSAN edge detector when used for finding lines in the image.

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''.

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.

This assumes that the USAN is a contiguous region. The refinements described later are designed to enforce this contiguity.

These images are only 128 by 128 in size.

Sometimes even some structure in the imaged world is treated as unwanted ``noise''.

This is assuming digital storage and not analog.

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.

All brightness values mentioned are within an image brightness scale of 0 to 255.

LaTeX2HTML conversion by Steve Smith (steve@fmrib.ox.ac.uk)