MarrHildrethAnsatz

MarrHildrethAnsatz is an edge-detection method introduced by David Marr and Ellen Hildreth in 1980, and is commonly referred to as the Marr–Hildreth operator or the Laplacian of Gaussian edge detector. It embodies a scale-space approach to edge detection, aiming to locate edges while suppressing noise by smoothing prior to differentiation.

The method applies a Gaussian blur to the image to reduce noise, then computes the Laplacian of the smoothed image. Edges are identified at locations where the Laplacian response crosses zero, i.e., where the second derivative changes sign. Because edge features can appear at multiple scales, the Marr–Hildreth Ansatz often uses a bank of Laplacian-of-Gaussian filters with different standard deviations, producing a multi-scale edge map. A threshold is typically applied to the LoG response or to the zero-crossings to filter weak edges, and sometimes non-maximum suppression is used to refine edge localization.

Relation and influence: The approach is foundational in scale-space theory and influenced later detectors such as the Canny edge detector. Its limitations include sensitivity to the choice of scale and threshold, potential poor localization compared with modern methods, and substantial computation when multiple scales are used. Despite these, the MarrHildrethAnsatz remains a landmark concept in early computer vision and in discussions of multi-scale edge detection.