Surf operator (1)

Surf operator, refer to the explanation of this article http://www.ipol.im/pub/art/2015/69/

SURF is the meaning of the speeded up robust Features accelerated robust feature.

The source code and the online demo is accessible at the Ipol Web page of this article1. The
Proposed implementation of the SURF algorithm is written in C + + Iso/ansi. It performs
Features extraction from digital images and provides local correspondences for a pair of images. The article mentions the polar geometry consistency to remove the mis-match point

An epipolar geometric consistency checking may additionally being used to discard mismatches
When considering and pictures from the same scene. This optional post-processing uses the ORSA algorithm Baidu no, Asift algorithm
ORSA algorithm by B. Stival and L. Moisan [International Journal of Computer Vision, 57
(2004), pp. 201{218].

1 Introduction
1.1 Context, motivation and Previous work
Over the last decade, the most successful algorithms to address various computer vision problems has
been based on local, ane-invariant descriptions of images. The targeted applications encompass,
But is not limited to, image stitching and registration, image matching and comparison, indexation
and classication, depth estimation and reconstruction. Like many image processing approaches,
A popular and ecient methodology is to extract and compare the local patches from dierent images.
However, in order to design fast algorithms and obtain compact and locally invariant representations,
Some selection criteria and normalization procedures are required. A sparse representation of the
Image is also necessary to avoid extensive patch-wise comparisons this would be computationally
Expensive. The main challenges is thus to keep more salient features from images (such as corners,
BLOBs or edges) and then to build a local description of these features which are invariant to various
Perturbations, such as noisy measurements, photometric changes, or geometric transformation.
Such problems has been addressed since the early years of computer vision, resulting in a very
Prolic literature. Without being exhaustive, one may rst mention the famous Stephen-harris Harris corner point Lindeberg Multi-scale feature detection

Corner Detector [9], and the seminal work of Lindeberg in Multi-scale feature detection (see e.g. [12]).
Secondly, invariant local image description from Multi-scale analysis are a more recent Topic:sift
descriptors [+] {from which SURF [2] is largely inspired{be similarity invariant descriptors of an
Image that is also robust to noise and photometric the change. Some algorithms extend this framework
To fully ane transformation invariance [+], and dense representation [26].
The main interest of the SURF approach [2] studied in this paper are its fast approximation of the
SIFT method. It has been shown to share the same robustness and invariance while being faster to
Compute.

1.2 Outline and Algorithm overview
The SURF algorithm is in itself based on two consecutive steps (feature detection and description) Main Two step feature point detection and descriptors
That is described in Sections 4 and 5. The last step was specic to the application targeted. In this
Paper, we chose image matching as an illustration (Sections 5.4 and 6).
Multi-scale analysis Similarly to many other approaches, such as the SIFT method [a], the
Detection of features in SURF relies on a scale-space representation, combined with first and second multi-scale analysis dependent and multi-spatial representations, based on one-order
Order dierential operators. The originality of the SURF algorithm (speeded up robust Features) are and second-order differential operations
That these operations is speeded up by the using of the box lters techniques (see e.g. [+]) that is surf operator accelerates multiple by box filter Scale
described in section 2. For this reason, we'll use the term box-space to distinguish it from the usual analysis, distinguishing it from the normal Gaussian scale space.
Gaussian Scale-space. While the Gaussian scale space was obtained by convolution of the initial images the Gaussian dimension is convolution of different Gaussian nuclei
With Gaussian Kernels, the discrete box-space are also obtained by convolving the original image with discrete box space is a photo filter with different scales of convolution
Box Lters at various scales. A comparison between these and scale-spaces are proposed in section 3.
Feature detection During The detection step, the local maxima in the box-space of the \determinant
of Hessian "operator is used to select Interest point candidates (Section 4). These candidates local maximum value of box filter space using Hessian
Was then validated if the response is above a given threshold. Both the scale and location of these
Candidates is then rened using quadratic tting. Typically, a few hundred interest points are positioned by curve fitting
Detected in a megapixel image.
Feature Description The purpose of the next step described in Section 5 are to build a descriptor describe the affine invariant with the domain variable for each point, based on the viewpoint
Of the neighborhood of each point of interest, is invariant to view-point changes. Thanks to

Multi-scale analysis, the selection of these points in the Box-space provides scale and translation multi-scale space will cause scaling and panning to be the same
Invariance. To achieve rotation invariance, a dominant orientation was dened by considering the local rotation is unchanged, the partial gradient direction is determined
Gradient orientation distribution, estimated from Haar wavelets. Using a spatial localization grid, a
64-dimensional descriptor is then built, based on RST order statistics of Haar wavelets coecients.
Feature matching Finally, when considering the image matching task (e.g. for image registration,
Object detection, or image indexation), the local descriptors from several images is matched.
Exhaustive comparison is performed by computing the Euclidean distance between all potential
Matching pairs. A Nearest-neighbor distance-ratio Matching criterion is then used to reduce mismatches,
Combined with an optional ransac-based technique [+] for geometric consistency
Checking.
Outline the rest of the paper is structured as follows
{Section 2 SURF multi-scale representation based on box lters;
{Section 3 Comparison and linear scale space analysis;
{Section 4 Interest points detection;
{Section 5 invariant descriptor construction and comparison;
{Section 6 experimental validation and comparison with other approaches.

Surf operator (1)