Feature Detection

Edge Detection¶

Remember to smooth the image before edge detection, otherwise the noise would affect the result.

Notice that:

\[ \frac{d}{dx}(f*g)=f*\frac{d}{dx}g \]

so we can apply gaussian derivative kernel on the image.

\[ ||\nabla f||=\sqrt{(\frac{\partial f}{\partial x})^2+(\frac{\partial f}{\partial y})^2} \]

直接使用 gradient magnitude 产生的边缘过厚, 我们采用如下方式将其变细: 对于每个点, 只保留边的方向上梯度幅值最大的点.

> 0.7 认为是边缘
< 0.3 认为不是边缘
中间认为是弱边.

Weak edges that are connected to strong edges will be actual/real edges.

Weak edges that are not connected to strong edges will be removed

核心观察: 考虑一个窗口内的像素, 角点位置窗口在各个方向移动后像素值均有很大变化.

Use Taylor Series to simplify the calculation

M 的特征值反映了 E 在各个方向的变化幅度

how to make it equivariant with scaling? -- Gaussian Pyramids!

Blobs are regions in a digital image that differ in properties, such as brightness or color, compared to surrounding regions.

Blobs have fixed positions and sizes, can be localized, and are good interest points.