This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.

A Computational Approach to Edge Detection

A snake is an energy-minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. Snakes are active contour models: they lock onto nearby edges, localizing them accurately. Scale-space continuation can be used to enlarge the capture region surrounding a feature. Snakes provide a unified account of a number of visual problems, including detection of edges, lines, and subjective contours; motion tracking; and stereo matching. We have used snakes successfully for interactive interpretation, in which user-imposed constraint forces guide the snake near features of interest.

/pdf/snakes-active-contour-models-2cuxgoykah.pdf

Snakes : Active Contour Models

In this paper, we present a novel scale- and rotation-invariant interest point detector and descriptor, coined SURF (Speeded Up Robust Features). It approximates or even outperforms previously proposed schemes with respect to repeatability, distinctiveness, and robustness, yet can be computed and compared much faster.

This is achieved by relying on integral images for image convolutions; by building on the strengths of the leading existing detectors and descriptors (in casu, using a Hessian matrix-based measure for the detector, and a distribution-based descriptor); and by simplifying these methods to the essential. This leads to a combination of novel detection, description, and matching steps. The paper presents experimental results on a standard evaluation set, as well as on imagery obtained in the context of a real-life object recognition application. Both show SURF's strong performance.

/pdf/surf-speeded-up-robust-features-1fje09jteo.pdf

SURF: speeded up robust features

http://library.utia.cas.cz/prace/20030125.pdf

Image registration methods: a survey

This paper investigates two fundamental problems in computer vision: contour detection and image segmentation. We present state-of-the-art algorithms for both of these tasks. Our contour detector combines multiple local cues into a globalization framework based on spectral clustering. Our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree. In this manner, we reduce the problem of image segmentation to that of contour detection. Extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms. The automatically generated hierarchical segmentations can be interactively refined by user-specified annotations. Computation at multiple image resolutions provides a means of coupling our system to recognition applications.

/pdf/contour-detection-and-hierarchical-image-segmentation-2ejknw01zo.pdf

Contour Detection and Hierarchical Image Segmentation

Perceptual studies suggest that the visual system may use a rigidity assumption in its recovery of three-dimensional structure from motion. Ullman [ Perception13, 255 ( 1984)] recently proposed a computational scheme that uses this assumption to recover the structure of rigid and nonrigid objects in motion. The scheme assumes the input to be discrete positions of elements in motion, under orthographic projection. We present formulations of Ullman’s method that use velocity information and perspective projection in the recovery of structure. Theoretical and computer analyses show that the velocity-based formulations provide a rough estimate of structure quickly but are not robust over an extended time. The stable long-term recovery of structure requires disparate views of moving objects.

Incremental rigidity scheme for recovering structure from motion: position-based versus velocity-based formulations

We present psychophysical experiments that measure the accuracy of perceived 3D structure derived from relative image motion. The experiments are motivated by Ullman''s incremental rigidity scheme, which builds up 3D structure incrementally over an extended time. Our main conclusions are: first, the human system derives an accurate model of the relative depths of moving points, even in the presence of noise; second, the accuracy of 3D structure improves with time, eventually reaching a plateau; and third, the 3D structure currently perceived depends on previous 3D models. Through computer simulations, we relate the psychophysical observations to the behavior of Ullman''s model.

/pdf/the-perceptual-buildup-of-three-dimensional-structure-from-1yx5fsoeg8.pdf

The Perceptual Buildup of Three-Dimensional Structure from Motion

https://cs.wellesley.edu/~vision/pubs/sfm2.pdf

Structure-from-motion: Perceptual evidence for surface interpolation

https://cs.wellesley.edu/~vision/pubs/sfm1.pdf

Recovering Three-Dimensional Structure from Motion with Surface Reconstruction

The computational approach to the study of vision inquires directly into the sort of information processing needed to extract important information from the changing visual image---information such as the three-dimensional structure and movement of objects in the scene, or the color and texture of object surfaces. An important contribution that computational studies have made is to show how difficult vision is to perform, and how complex are the processes needed to perform visual tasks successfully. This article reviews some computational studies of vision, focusing on edge detection, binocular stereo, motion analysis, intermediate vision, and object recognition.

Ellen C. Hildreth

Papers

Incremental rigidity scheme for recovering structure from motion: position-based versus velocity-based formulations

The Perceptual Buildup of Three-Dimensional Structure from Motion

Structure-from-motion: Perceptual evidence for surface interpolation

Recovering Three-Dimensional Structure from Motion with Surface Reconstruction

The computational study of vision