4

The answer is simple, the Sobel Filter is a composition of Lows Pass Filter (LPF) and High Pass Filter (HPF). The composition is done by convolution. Now, indeed the LPF presented above $ {\left[ 1, 2, 1 \right]}^{T} $ has amplification in the DC value (Its sum is 4 so the amplification is 4). Yet it is convolved with an HPF filter which rejects the DC ...


3

In the classic framework both the Smoothing and the Difference Filter are applied using Convolution. Since it is done using convolution it implies the operation is Linear Spatially Invariant (LSI). LSI operators can be applied in any order and the result will be the same. This is also a result of the commutativity property of the convolution operator. Let's ...


3

Unless mentioned otherwise withing the context the classic interpretation of Second Derivative Gaussian Filter is indeed (a) in your question: $$ L \left( x, y, \theta \right) = \cos \left( \theta \right) {g}_{xx} \left( x, y \right) + \sin \left( \theta \right) {g}_{yy} \left( x, y \right) $$


2

I would consider the notion of edge, with respect to that of contour, in the same relation as words to a sentence. An edge is a distinctive element of an image (a color change, a border cut, a shadow, an occlusion). Here, from top to bottom: surface normal, depeth, illumination, shadow. But sometimes, this does not fully takes advantage of the whole ...


2

Contour is the edge closing an object. So you can think as higher level of edge detection. So if an edge define an object it becomes a contour.


2

Not sure how you do it in python, but the idea can be as simple as the following: After you select a random point on the edge pixel, calculate the horizontal gradient and the vertical gradient with this pixel at the centre of the gradient filter. The width of the kernel for the gradient filters will depend on the maximum width of the edges. For example if ...


2

The approach seems reasonable. Indeed doing edge detection in weighted RGB channel is the classic approach (Though you could also employ more advance methods, See Edge Detection on a Color Image). I think you could achieve great results if you also look specifically for oval shapes then you reduce the chances for false positives. Color identification in ...


1

My suggestion: find the center, calculate the distance of each pixel to the center. If a given distance is too (above threshold) different from the neighborhood then it's a defect. Other possibility is to fit a figure model if you always have the same shape and then calculate the error.


1

Couple of approaches come to mind: you could pick an arbitrary "first" red pixel, then take a square of say 5×5 pixels around it, and simply figure out which quadratic function is a best fit for these, and infer the curvature from that. Pick an arbitrary direction to start from that point and pick the next pixels; calculate the curvature of the 5×5 ...


1

I have been looking again into this question. The tensor product doesn't really have such a special meaning here. According to Nonlinear Structure Tensors: "Although this tensor product contains no more information than the gradient itself, it has the advantage that it can be smoothed without cancellation effects in areas where gradients have opposite ...


1

You need to think 3D. You are looking at the domain and the range is the intensity. The first step is to fix the outliers as you have them. For each cell in the plane, calculate the average of the neighbors (before their adjustments). If the cell value exceeds a specified threshold, limit the value to that threshold. Next do four smoothing passes: ...


1

Just a couple of thoughts: That sounds like the classical application for a Kalman filter: you have one gaussian-overlaid signal that "develops" over the columns If you have a signal model for your signal of interest, a parametric estimator might indeed be the best choice here. You could write a likelihood function for each observation column $\...


1

"Need" or "Want"? Q1: The second derivative avoids the problem of a gradually changing color being "greyish". Q2: Yes. Here is one: After advice about detecting focus quality of objects in a photo detected using YoloV3 It is based on how planar the color. Very planar means no edge. There are many, many other variations of these techniques possible.


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