SURF算子(1)

SURF算子，参考这篇文章的解释http://www.ipol.im/pub/art/2015/69/

SURF 是   Speeded Up Robust Features 加速鲁棒特征的含义。

The source code and the online demo are 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.   文章提到了极几何一致性去去掉误匹配点

An epipolar geometric consistency checking may additionally be used to discard mismatches              
when considering two pictures from the same scene. This optional post-processing uses the           ORSA算法 百度没有，ASift算法
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 have
been based on local, ane-invariant descriptions of images. The targeted applications encompass,
but are not limited to, image stitching and registration, image matching and comparison, indexation
and classication, depth estimation and 3-D reconstruction. Like many image processing approaches,
a popular and ecient methodology is to extract and compare 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 that would be computationally
expensive. The main challenges are thus to keep most salient features from images (such as corners,
blobs or edges) and then to build a local description of these features which is invariant to various
perturbations, such as noisy measurements, photometric changes, or geometric transformation.
Such problems have 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角点 lindeberg多尺度特征检测

corner detector [9], and the seminal work of Lindeberg on multi-scale feature detection (see e.g. [12]).
Secondly, invariant local image description from multi-scale analysis is a more recent topic: SIFT
descriptors [15] {from which SURF [2] is largely inspired{ are similarity invariant descriptors of an           
image that are also robust to noise and photometric change. Some algorithms extend this framework
to fully ane transformation invariance [18, 28], and dense representation [26].
The main interest of the SURF approach [2] studied in this paper is 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)     主要两个步骤 特征点检测和描述子
that are described in Sections 4 and 5. The last step is 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 [15], the
detection of features in SURF relies on a scale-space representation, combined with first and second    多尺度分析依赖与多空间表述，基于一阶
order dierential operators. The originality of the SURF algorithm (Speeded Up Robust Features) is        和二阶差分运算
that these operations are speeded up by the use of box lters techniques (see e.g. [25], [27]) that are    SURF算子通过盒子滤波器加速多尺度
described in Section 2. For this reason, we will use the term box-space to distinguish it from the usual    分析，区别于普通的高斯尺度空间。
Gaussian scale-space. While the Gaussian scale space is obtained by convolution of the initial images      高斯尺度空间是卷积不同高斯核
with Gaussian kernels, the discrete box-space is also obtained by convolving the original image with 离散盒子空间是卷积不同尺度的合照滤波器
box lters at various scales. A comparison between these two scale-spaces is proposed in Section 3.
Feature detection During the detection step, the local maxima in the box-space of the \determinant   
of Hessian" operator are used to select interest point candidates (Section 4). These candidates  用Hessian定位盒子滤波器空间的局部最大值
are then validated if the response is above a given threshold. Both the scale and location of these
candidates are then rened using quadratic tting. Typically, a few hundred interest points are   通过曲线拟合定位
detected in a megapixel image.
Feature description The purpose of the next step described in Section 5 is to build a descriptor  用每个点的领域变域来描述 仿射不变，基于视点
of the neighborhood of each point of interest that is invariant to view-point changes. Thanks to

multi-scale analysis, the selection of these points in the box-space provides scale and translation 多尺度空间会导致尺度和平移不变
invariance. To achieve rotation invariance, a dominant orientation is dened by considering the local  旋转不变，局部梯度方向决定
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 are 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 [21, 20] 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 with 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.