Shape Feature Extraction-Hu Invariant moment (reproduced)

[OriginalPart reprinted ]:Http://blog.csdn.net/wrj19860202/archive/2011/04/16/6327094.aspx

When the image function is continuous, the p + q geometric moment (Standard moment) of the image is defined:

The center distance of the p + q level is defined:

 

And represent the center of gravity of the image,

For discrete digital images, the sum number is used to replace points:

 

 

And are respectively the height and width of the image;

The center distance of normalization is defined:

Where

(Ps_yang: the value of P here is controversial. different formulas are given in different literature [Study of invariant moment algorithms. Ding Mingyue. huake.

The main controversy lies in whether to add 1 after P. Personal programming practices found that adding 1 should be the right choice.

In the original Hu Moment: visual pattern recognition by moment invariants, the original formula cannot be found. There is no detailed explanation of the relevant books. Hope you can give me some advice .)

Seven invariant moments are constructed using second-and third-order normalized center moment:

 

These seven immutations constitute a set of feature quantities. hu. M. K proved in 1962 that they have rotation, scaling, and moving immutability.

In fact, in the process of recognizing an object in an image, it is only better than immutability. The other several immutability moments bring about a large error, some scholars believe that only the immutations based on the second moment can describe two-dimensional objects with real rotation, scaling, and shift immutability (and are both composed of the second moment ). However, I have not proved whether it is true or not.

The feature quantity composed of Hu moments identifies images. The advantage is that the image recognition speed is fast. The disadvantage is that the recognition rate is low. I have done Gesture Recognition and the recognition rate is about 30% for the split gesture profile, for images with rich textures, the recognition rate is even worse, with only around 10%. This is due to the fact that Hu Moment immutations only use low-order moments (at most, third-order moments), and the image details are not well described, resulting in incomplete descriptions of the image.

Hu moments are generally used to recognize large objects in an image. They describe the shape of an object, and the texture features of the image cannot be too complex. The image recognizes the shape of a fruit, or the recognition of simple characters in the license plate will be better.

 

Shape Feature Extraction-Hu Invariant moment (reproduced)