拉普拉斯的高斯滤波器使用 [英] Laplacian of gaussian filter use

问题描述

这是LoG过滤的公式：
alt text http：/ /homepages.inf.ed.ac.uk/rbf/HIPR2/eqns/eqnlog2.gif

This is a formula for LoG filtering: alt text http://homepages.inf.ed.ac.uk/rbf/HIPR2/eqns/eqnlog2.gif

同样在使用LoG过滤的应用程序中，我看到该功能是仅使用一个参数调用：
sigma（σ）。
我想尝试使用该公式进行LoG过滤（之前的尝试是通过高斯滤波器，然后是laplacian过滤器，带有一些过滤器窗口大小）
但是看看那个公式我无法理解过滤器的大小与此公式相关，是否意味着过滤器尺寸是固定的？
你能解释一下如何使用吗？

Also in applications with LoG filtering I see that function is called with only one parameter: sigma(σ). I want to try LoG filtering using that formula (previous attempt was by gaussian filter and then laplacian filter with some filter-window size ) But looking at that formula I can't understand how the size of filter is connected with this formula, does it mean that the filter size is fixed? Can you explain how to use it?

推荐答案

你现在可能已经从其他答案中找到了答案和链接，LoG过滤器检测图像中的边和线。仍然缺少的是对σ是什么的解释。

As you've probably figured out by now from the other answers and links, LoG filter detects edges and lines in the image. What is still missing is an explanation of what σ is.

σ是过滤器的比例。一个像素宽的线是线还是噪声？一条线是6像素宽一条线还是一条有两条不同平行边的物体？渐变是从黑色变为白色，跨越6或8像素的边缘还是仅仅是渐变？这是你必须要决定的事情，σ的价值反映了你的决定— σ越大，线条越宽，边缘越平滑，忽略更多噪声。

σ is the scale of the filter. Is a one-pixel-wide line a line or noise? Is a line 6 pixels wide a line or an object with two distinct parallel edges? Is a gradient that changes from black to white across 6 or 8 pixels an edge or just a gradient? It's something you have to decide, and the value of σ reflects your decision — the larger σ is the wider are the lines, the smoother the edges, and more noise is ignored.

不要混淆滤波器的比例（σ）和离散近似的大小（通常称为模板）。在Paul的链接σ= 1.4，模板尺寸为9虽然使用4σ到6σ的模板尺寸通常是合理的，但这两个量是相当独立的。较大的模板可以提供更好的滤波器近似值，但在大多数情况下，您不需要非常好的近似值。

Do not get confused between the scale of the filter (σ) and the size of the discrete approximation (usually called stencil). In Paul's link σ=1.4 and the stencil size is 9. While it is usually reasonable to use stencil size of 4σ to 6σ, these two quantities are quite independent. A larger stencil provides better approximation of the filter, but in most cases you don't need a very good approximation.

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