10-04-2012, 02:21 PM
OpenSURF Library
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SURF: Speeded Up Robust Features
In this document, the SURF detector-descriptor scheme used in the OpenSURF library
is discussed in detail. First the algorithm is analysed from a theoretical standpoint to
provide a detailed overview of how and why it works. Next the design and development
choices for the implementation of the library are discussed and justied.
Integral Images
Much of the performance increase in SURF can be attributed to the use of an intermediate
image representation known as the \Integral Image" [7]. The integral image is computed
rapidly from an input image and is used to speed up the calculation of any upright
rectangular area. Given an input image I and a point (x; y) the integral image IP is
calculated by the sum of the values between the point and the origin. Formally this can
be dened by the formula:
The Hessian
The SURF detector is based on the determinant of the Hessian matrix. In order to
motivate the use of the Hessian, we consider a continuous function of two variables such
that the value of the function at (x; y) is given by f(x; y). The Hessian matrix, H, is the
matrix of partial derivates of the function f.
Constructing the Scale-Space
In order to detect interest points using the determinant of Hessian it is rst necessary to
introduce the notion of a scale-space. A scale-space is a continuous function which can be
used to nd extrema across all possible scales [8]. In computer vision the scale-space is
typically implemented as an image pyramid where the input image is iteratively convolved
with Gaussian kernel and repeatedly sub-sampled (reduced in size).
Accurate Interest Point Localisation
The task of localising the scale and rotation invariant interest points in the image can be
divided into three steps.
Interest Point Descriptor
The SURF descriptor describes how the pixel intensities are distributed within a scale
dependent neighbourhood of each interest point detected by the Fast-Hessian. This ap-
proach is similar to that of SIFT [4] but integral images used in conjunction with lters
known as Haar wavelets are used in order to increase robustness and decrease computa-
tion time.
Results
In this section we test the SURF library using an image dataset provided by Kristian
Mikolajczyk3. This dataset contains sequences of images which exhibit real geometric and
photometric transformations, such as scaling, rotation, illumination and JPEG compres-
sion. Comparing the results of various detector-descriptors is a complex task and a full
body of work in itself. Mikolajczyk [5, 6] compared the most widely used detectors and
descriptors and Bay [1] used the same testing strategy to show how SURF outperforms
its predecessors.