---
title: "An Optimal Scale for Edge Detection"
authors:
  - "Davi Geiger"
  - "Tomaso A. Poggio"
doi: ""
url: "https://ijcai.org/proceedings/1987/150"
pdf: "https://ijcai.org/proceedings/1987/0150.pdf"
venue: "Proceedings of the Tenth International Joint Conference on Artificial Intelligence"
year: 1987
pages: "745-747"
track: "Perception"
keywords:
---

# An Optimal Scale for Edge Detection

Davi Geiger, Tomaso A. Poggio

*Proceedings of the Tenth International Joint Conference on Artificial Intelligence*, pages 745-747.

## Abstract

Many problems in earl y vision are ill posed 1 . Edge detection is a typical example. This paper applies regularization techniques to the problem of edge detection. We derive an optimal filter for edge detection with a size controlled by .the regularization parameter A and compare it to the Gaussian filter. A formula relating the signal-to-noise ratio to the parameter A is derived from regularization analysis, showing that the scale of the filter is a function of the signal-to-noise ratio. We also discuss the method of Generalized Cross Validation for obtaining the optimal filter scale. Finally, we use our framework to explain two perceptual phenomena: coarsely quantized images becoming recognizable by either blurring or adding noise.