Deriche edge detector

• Detection quality – all existing edges should be marked and no false detection should occur.
• Accuracy - the marked edges should be as close to the edges in the real image as possible.
• Unambiguity - a given edge in the image should only be marked once. No multiple responses to one edge in the real image should occur.

For this reason, this algorithm is often referred to as Canny-Deriche detector.

Differences between Canny and Deriche edge detector

Deriche edge detector, like Canny edge detector, consists of the following 4 steps:

1. Smoothing
2. Calculation of magnitude and gradient direction
3. Non-maximum suppression
4. Hysteresis thresholding (using two thresholds)

The essential difference is in the implementation of the first two steps of the algorithm. Unlike the Canny edge detector, Deriche edge detector uses the IIR filter in the form:

${\displaystyle f(x)=\frac{S}{\omega }{e}^{-\alpha |x|}\sin \omega x}$

The filter optimizes the Canny criteria. As is evident from the preceding formula, the most effective filter is obtained when the value of ${\displaystyle \omega }$ approaches 0. Such filter then uses the formula:

${\displaystyle f(x)=Sx{e}^{-\alpha |x|}}$

The advantage of such a filter is that it can be adapted to the characteristics of the processed image using only one parameter. If the value of α is small (usually between 0.25 and 0.5), it results in better detection. On the other hand, better localization is achieved when the parameter has a higher value (around 2 or 3). For most of the normal cases parameter value of around 1 is recommended.

Using the IIR filter makes sense especially in cases where the processed image is noisy or a large amount of smoothing is required (which leads to large convolution kernel for FIR filter). In these cases, the Deriche detector has considerable advantage over the Canny detector, because it is able to process images in a short constant time independent of the desired amount of smoothing.