β Scribed by Rajiv Mehrotra; Shiming Zhan
No coin nor oath required. For personal study only.
Consequently, there has been a substantial effort to study A commonly employed computational approach to the design the edge detection problem.
Early edge detection techniques [20,24] use local operaas an optimization problem by defining a penalty function and tors to estimate the first derivative or the gradient of the constraints in terms of performance measures such as signalimage function at each point. The local maxima of the to-noise ratio (SNR), spurious response, and edge localization. gradient are considered edges. In recent years, several so-Unfortunately, this approach generally results in highly comphisticated edge detection techniques have been proposed.
Marr and Hildreth [15] proposed the Laplacian of Gaussian higher dimensional edge detection. Therefore, most of the pre-(LoG) detector. The zero-crossings in an LoG filtered imviously reported efforts have either proposed 1D optimal detecage are considered edge points. The Gaussian function is tors or their approximations to higher dimensions. This paper presents a computational approach to optimal edge detector selected because it optimizes the uncertainty relation for design, which utilizes some desirable properties of detector the localization requirements in the spatial and the frefunctions to simplify the optimization problems. Specifically, quency domains. Since edges occur over a wide range of a zero-crossing-based 2D edge detector, which is the Laplacian scales, an LoG detector tuned to different scales can be of a rotationally invariant finite support function with a used to detect edges at multiple scales. Yuille and Poggio smooth boundary and yields optimal performance with re-[27] and Babaud et al. [1] established that the Gaussian spect to a penalty function defined in terms of a simplified function is the only detector which does not generate ge-SNR measure and Canny's edge localization, and spurious reneric zero-crossings with the increase in scale. Lu and Jain sponse measures. The performance of the proposed 2D step edge detector is theoretically and empirically analyzed and [14] studied the performance of the LoG detector in scale compared to that of the Laplacian of Gaussian detector. Exspace with respect to the influence of the neighboring edges perimental results with some synthetic and real images are on each other. Haralick [8] proposed a facet model-based presented.
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