Edge detection is a fundamental problem of computer vision and has been widely investigated. We propose a new framework for edge detection based on edge profiles.Our model, based on one-dimensional qualitative edge profile fitting and edge consistency, will produce one continuous edge from an initial seed point. A "profile" is defined as a finite cross-section of a two-dimensional image along a line segment. "Edge consistency" means that all the profiles on the same edge should be consistent. Appropriate evaluation functions are needed for different types of edge profiles, such as step edges, ramp edges, etc. An evaluation function must meet the requirement that it will produce local minima at the positions where edges of a given type occurs in the profile. Instead of subjective thresholding, image noise is measured statistically and used as a systematic way of filtering false edges. We describe our method as "qualitative edge profile fitting" because it is not based on arbitrary thresolding. Once an edge point is localized, it can be extended into an edge by matching compatible profiles. Two profiles are considered compatible as long as their average di erence is within the noise measurement. Another feature of our approach is its subpixel accuracy. The utilization of profiles and noise-induced threshold selection make tasks such as joining broken edges more objective. We develop the necessary algorithms and implement them. Different evaluation functions are constructed for different edge models and experimented on different one-dimensional profiles. The edge detector, using these evaluation functions, is then examined using different images and under different noise conditions.