Johan De Vriendt

Accuracy of the zero crossings of the second directional derivative as an edge detector

In this paper the accuracy of the second directional derivative edge detector is analyzed, based on a number of idealized edge models. The results are compared with those for the Laplacian edge detector. Errors are shown to be small under a number of conditions. These conditions are less severe for the second directional derivative than for the Laplacian edge detector. Spurious or phantom edges can be removed by checking the sign of the third directional derivative, though this is not enough to remove all large errors. Indeed, it is also shown that large errors will be obtained if no threshold is set on the magnitude of a third order derivative.

Fast computation of unbiased intensity derivatives in images using separable filters

In this paper we prove that all high order non-biased spatial intensity derivative operators in images can be computed using linear combinations of separable filters. The separable filters are the same as those used by Haralick (1984), but different linear combinations are taken. A comparison of the number of operations necessary to compute the derivatives using separable and non-separable filters is made. The conclusion of our analysis is that the optimal way to compute the needed derivatives depends on which derivatives we have to compute, on the size of the window and on the order of expansion. Finally, we discuss the performance of an edge detector using these derivatives for unsmoothed and smoothed step edges.

Effect of sampling, quantization and noise on the performance of the second directional derivative edge detector

Berzins [2] and De Vriendt [14] studied the processes that influence the performance of the Laplacian and the second directional derivative edge detector in the continuous domain. In this paper the influence of sampling, quantization and noise is studied in the discrete domain for the second directional derivative edge detector. The results are compared with those for the Laplacian edge detector. The smoothing and derivative operations are implemented by FIR digital filters. Two sampling processes are considered: a square aperture and a Gaussian smoothing process. The influence of sampling can be limited by increasing the spread σ of the smoothing filter. Though, σ should not be chosen too large because of the influence of nearby edges. The quantization of the intensity function introduces an uncertainty in the edge location. The uncertainty is larger than the error due to sampling if the step height is small. We also prove that the second directional derivative is less sensitive to noise than the Laplacian. An increase of σ slightly reduces the variation of the edge location.

Derivation of the third-order directional derivative

Abstract We give an easy derivation of the third order directional derivative in the direction of the gradient of the intensity function. The obtained formula is a correction of the formula found by Clark (1989).

Motion estimation of curves: experimental results using regularization techniques

In this paper we compare the use of first and second order stabilizer functionals for the estimation of the motion of curves for real images. We discuss some implementation aspects which influences the performance. The algorithm is tested on a number of image sequences with known motion (quantitatively) and with motions which are only qualitatively known. The accuracy with which the motion of curves can be estimated is about 0.2 pixels for images undergoing relatively large motions (translations, expansions and rotations).