Question

Let I be an image where edge detection is to be performed. Mark all the statements that are

A) The Canny edge detection algorithm detects edges where the directional derivative along the direction of the gradient has a local maximum.
B) Smoothing before edge detection is not com- monly employed because it makes the detected edges less accurate.
C) A Gaussian image pyramid is a useful way for processing an image at multiple scales.
D) When designing a smoothing filter using a Gaussian with a standard deviation of 5, the size of the Gaussian filter should be set to 5 x 5 to match the rounded value of the standard deviation.
E) The image derivative in the X direction may be computed using two ID convolutions.
F) Smoothing before edge detection is important to reduce noise.

Answer 1

In edge detection of an image I, the Canny edge detection algorithm is correctly described, smoothing is important to reduce noise, and a Gaussian image pyramid is useful for multi-scale processing. However, a Gaussian filter size should be much larger than the standard deviation, and image derivatives can be computed using 1D convolutions.

Step-by-step explanation:

Let's evaluate the statements about edge detection in an image I:

• A) True. The Canny edge detection algorithm detects edges in an image by finding the local maxima of the gradient of the image. The edges are where the directional derivative in the direction of the gradient is largest.
• B) False. Smoothing is often used before edge detection to reduce noise which can cause false edges. However, excessive smoothing can indeed make the detected edges less accurate by blurring them too much.
• C) True. A Gaussian image pyramid allows an image to be processed at multiple scales, which is beneficial for detecting edges that may occur at different scales.
• D) False. When designing a Gaussian filter, the size of the filter should be much larger than the standard deviation to effectively capture the characteristics of the Gaussian distribution. Typically, a filter size is chosen to be around 6 times the standard deviation, rounded up to the nearest odd number to have a central pixel.
• E) True. Image derivatives in any direction, including the X direction, can be computed by convolving the image with appropriate one-dimensional kernels, first in one direction (e.g., horizontally) and then in the other direction (e.g., vertically).
• F) True. Smoothing before edge detection is crucial to reduce noise in the image, which otherwise could be detected as false edges.

Understanding the principles of edge detection is fundamental in computer vision and image processing to enhance the quality and accuracy of the detected images.