[Reading notes] computer vision and algorithm application Chapter 4.2 edge

4.2 Edge

Although feature points are useful for finding the position of an image that can be precisely matched in 2D, the edge points are richer and often contain important semantic associations.

4.2.1 Edge Detection

• The edges appear between areas with different colors, brightness, or textures.
• Usually only local information is used to detect edges more appropriately
• The slope and direction of a surface is achieved by its gradient.

The local gradient vector J points to the fast rising (steepest ascent) direction of the luminance function, whose amplitude is an indication of its slope or the intensity of the change, which is directed toward the direction perpendicular to its local contour.

• Because the high frequency part of the noise and signal ratio is large, so the derivative of the image to emphasize the high frequency of the part thus amplified the noise. This requires smoothing the image with a low-pass filter before the gradient is computed. Because the response of the edge detector is independent of direction, a smoothing filter with a circular symmetry is required. The Gaussian function is the only separable circular symmetric filter, so most edge detection algorithms use it.

The parameter σ reflects the bandwidth of the Gaussian function.

• It is hoped that the continuous gradient image will be thinned so that it only exists on an isolated edge, that is, only a single pixel is distributed in a discrete position along the contour of the edge. This can be obtained by finding the maximum value of the edge response (gradient amplitude) in the vertical direction of the edge direction (gradient direction).
• The maximum value above corresponds to the number of directions of the intensity field in the direction of the gradient, and then 0 points are searched.

In practice, the Gauss derivative convolution is often converted to Gaussian differential (DoG), because the shape of its kernel function is similar in nature.

• Scale selection and fuzzy estimation:

1. The difference between the derivative, Laplace and Gaussian filters requires the selection of the spatial scale parameter σ.
2. Only strong edges are detected, the bandwidth of the filter can be determined from the noise characteristics of the image, and the detection of edges at different resolutions requires a scale-space approach to find the edges on different scales.
3. Elder and Zucker (1998) gives a solution: given a noise level, their approach can reliably detect the minimum scale of the edge for each pixel calculation.

• Color Edge Detection

1. The grayscale detector combines the results of independent output in each color space-the problem is that the signed gradient may be offset.
2. Alternatively, each color space is detected independently of the edges and then joined together-the problem is that it may cause the edges to be bold or double edges to be difficult to connect.
3. The better approach is to calculate the directed energy (oriented) in each color space, add the weighted directed energy and look for the best direction of their union-the direction derivative of the energy may not have a closed solution and cannot use the 0-point strategy. However, local color statistics can be estimated using the area around each pixel.
4. Combining edge feature Clues

4.2.2 Edge Connection

• If the edge is already detected by over 0 points of a function, then connecting the boundary element with the common endpoint is very straightforward (with a sequence table, a 2D array).
• If the edge is not detected at 0, you will need some tricks, such as looking at the direction of the adjacent boundary element when there is ambiguity.
• Threshold processing with lag: Allows tracked curves above higher thresholds to contain edges low to low thresholds.
• Arc length parameterization (ARC length parameterization): X (s), s represents the arc length on a curve.

The advantage of Arc-length parameterization is that it makes it easier to match and process operations.

4.2.3 Applications: Edge Editing and enhancement

• Edges can be used not only as a component of object recognition or as a matching feature, but also directly for image editing.

• Another potential application: enhance significant edges in cartoons or pen and ink.

[Reading notes] computer vision and algorithm application Chapter 4.2 edge