How can i measure shape elongation feature in matlab or python opencv? How can i measure shape elongation faeture in matlab or python opencv?
There is a function library or i have to implement to my own?
In case there is no function, i found this definition: 

"The less-common elongation shape factor is defined as the square root of the ratio of the two second moments in of the particle around its principal axes"

f_elong = sqrt (i2/i1)


Where i found these first and second moments?
In the Image Processing Toolbox for MATLAB there is a function called regionprops, which may be what you need. It takes a binary image, finds connected components in it, and returns various measurements of each connected component.  Here's a list of things it can compute:

Shape Measurements

  'Area'              'EulerNumber'       'Orientation'               
  'BoundingBox'       'Extent'            'Perimeter'          
  'Centroid'          'Extrema'           'PixelIdxList' 
  'ConvexArea'        'FilledArea'        'PixelList'
  'ConvexHull'        'FilledImage'       'Solidity' 
  'ConvexImage'       'Image'             'SubarrayIdx'            
  'Eccentricity'      'MajorAxisLength' 
  'EquivDiameter'     'MinorAxisLength'                   

Pixel Value Measurements (requires grayscale image as an input)

  'MaxIntensity'
  'MeanIntensity'
  'MinIntensity'
  'PixelValues'
  'WeightedCentroid'