To detect obstacles based on symmetry characteristics , according to general qualitative analysis methods , we can only know whether the obstacles are symmetrical , but here it is not enough to just use qualitative analysis of symmetry . We must be able to use mathematical methods to detect obstacles. For a quantitative description , the quantitative analysis of symmetry is introduced below. This paper uses the concept of continuous symmetry to establish a quantitative method to measure symmetry. A row of grayscale data in the image can be regarded as a one-dimensional function g(x) of the horizontal pixel coordinates ( we do not need to know what the function is, because our final calculation only uses this function value, which is similar to the feeling of a kernel function ).
Any function can be written as the sum of an even function and an odd function ,
Importance of odd and even functions:
The energy function of the odd and even functions is as follows:
Then perform the following normalization process on the dual function, as follows, so that its mean value is 0 ,
The measurement of symmetry defined using the energy function is as follows:
The symmetry measurement value is any number in the interval ( -1 , 1 ). S=1 means complete symmetry, S=0 means asymmetry, S=-1 means anti-symmetry. There is a one-to-one correspondence between the measure and the parameter .
The above formula needs to be implemented as code. A row of grayscale data in the image can be regarded as a one-dimensional function g(x) of the horizontal pixel coordinates.
The front car generally has strong horizontal symmetry, so a column of grayscale data of the detected rectangular roi that is suspected to be the front car can be accumulated separately as g(u).