Detection and matching of object using proposed signature - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 493

succeeding section is discussing SURF method because it is the most important one in the ob-
ject detection and matching ways.
The rest of this chapter is organized as follows. Section 2 introduces an overview on SURF.
A brief overview on image segmentation is discussed in Section 3 . In Section 4 , the proposed
algorithm of detection and matching has been illustrated. The algorithm's experimental res-
ults are detailed in Section 5 and the conclusion in Section 6 .
2 Overview on SURF method
The initial mention of SURF was by Bay in 2006. It has four major stages: Hessian matrix, loc-
alization of these points, orientation assignment, and descriptor, which is depended on Haar
wavelet response's sum [ 18 ] . In the first, Hessian matrix is based on detection in scale space
of interested points. Additionally, the determinant of Hessian matrix has used as a preference
to look for local maximum value, and the detection of SURF interested point is based on the-
ory of scale space. Equation (1) illustrates in details the components of Hessian matrix. In this
equation, there is a point X = ( x , y ) in an image I, the Hessian matrix H ( X , σ ) in X at scale σ has
deined as follows:
(1)
where L xx ( X , σ ) represents the convolution of the Gaussian second-order partial derivative.
δ 2 g ( σ )/ δx 2 with the image I in a point X , and similarly for L xy ( X , σ ) with δ 2 g ( σ )/ δxδy and L yy ( X , σ )
by δ 2 g ( σ )/ δy 2 .
To speed up the convolution, 9 × 9 box filter is utilized to approximate integral image and
the second-order Gaussian partial derivatives with σ = 1.2 [ 18 ] . The symbols D xx , D xy , and D yy ,
are denoting the convolution results' approximations. The determinant of Hessian matrix is
(2)
where w is recommended as 0.9, that is the relative weight of the filter responses [ 17 , 18 ] . The
step after is dividing the image into many regions, each one contains different scale image
templates.
The second stage is the interested point localization. First step in this stage is seting a
threshold to the detected Hessian matrix of extreme points. Second step, to obtain these points
a nonmaximum suppression in a 3 × 3 × 3 neighborhoods have applied. The bases of selecting
a feature point are that only the point with value bigger than the neighboring 26 points' value
has chosen as a feature point [ 18 ] .