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Image Visualization
Published in Alexandru Telea, Data Visualization, 2014
A last remark concerns the size of the neighborhoods involved in the various edge estimators discussed so far. The Sobel and Prewitt operators use 3 × 3 pixel neighborhoods to estimate first-order image derivatives, which are more stable compared to the 2 × 2 neighborhoods used by the Roberts operator. In terms of signal processing, it can be shown that the Sobel and Prewitt operators correspond to estimating derivatives on smoothed versions of the original image [Jain et al. 95]. In contrast, the Laplace operator uses a 3 × 3 neighborhood too, but this does imply signal smoothing: Estimating second-order derivatives requires larger neighborhoods by definition. If we want to perform additional smoothing when using Laplacian edge estimators, this involves using neighborhoods of a size exceeding 3 × 3. An example is the Marr-Hildreth operator, which is equivalent to computing the Laplacian of an image presmoothed with a Gaussian filter [Jain et al. 95], which uses a 5 × 5 pixel neighborhood. Since Gaussian smoothing eliminates high-frequency information, this type of operator yields more stable edge detection than directly applying the Laplacian.
Phase image-guided adaptive rotation-invariant feature point detector
Published in The Imaging Science Journal, 2023
Ahmed S. Mashaly, Tarek A. Mahmoud
For each non-homogenous pixel location of the input image , compute the following image derivatives: Compute the first image derivative in the horizontal direction using Sobel mask operator in Figure 6(a).Compute the first image derivative in the vertical direction using Sobel mask operator in Figure 6(b).Compute the phase image:.Compute the second image derivative in the horizontal direction using the mask operator of Figure 7(a).Compute the second image derivative in the vertical direction using the mask operator of Figure 7(b).Compute the second image derivative in the isotropic direction using the mask operator of Figure 7(c).The calculated phase image of the previous step is processed concerning the phase’s approximation chart shown in Figure 8. This step aims to define discrete edge orientations that could be used in the pre-feature point detection step as in Equation (18). The approximated phase image of Equation (18) is checked to mark the phase variation in the neighbouring pixels. This operation could be simplified as follows: Determine the associated pixels that have the same phase value in the neighbouring pixels (the pixels that belong to the same edge segment).Check if any other edge segments could be found in the neighbourhood pixels (the pixels that have the same phase value in the vertical, horizontal, and diagonal directions).If the number of edge segments found is greater than two. This means that the pixel under test presents a potential feature (corner) point.