ASIFT算法：超越SIFT的全仿射不变特征匹配

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本文档介绍了一种名为ASIFT (Aﬃne Scale-Invariant Feature Transform) 的算法，它是SIFT (Scale-Invariant Feature Transform) 算法的一种改进版本，旨在解决在物体识别问题中面对的全仿射不变性问题。SIFT算法原本着重于尺度、旋转和位移不变性，但ASIFT在此基础上进一步扩展，考虑了图像在不同相机位置下由于物体边界平滑或分段光滑引起的局部仿射变形。 ASIFT算法的设计背景是基于这样一个事实：当物体的边界是平滑的或由多个平滑部分组成时，其拍摄的图像在相机位置变化时会经历平滑的明显变形，这些变形可以通过局部仿射变换来近似。因此，将固态对象识别问题转化为在仿射变换下的图像局部特征计算具有重要意义。文章指出，ASIFT算法的主要改进在于它模拟了一个“完全仿射不变”的特性，这使得它在处理如缩放、旋转以及更复杂的仿射变换（包括扭曲）时更加有效和稳定。相比于原始的SIFT，ASIFT能够在各种情况下提供更为准确和鲁棒的特征匹配，这对于计算机视觉中的目标检测、物体识别、图像配准等任务来说是一大进步。该算法发表于2011年2月24日的《在线图像处理》(Image Processing Online)，并经过了提交、接受过程，遵循了ISSN 2105-1232的期刊标准。作者Guoshen Yu和Jean-Michel Morel分别来自法国的CMLA（ENSECachan）和CMAP（École Polytechnique），他们通过在线提供了补充材料、软件、数据集和在线演示，方便读者深入理解和使用ASIFT。截至2014年7月1日，ASIFT算法已经发展到了v0.5版本，并被归类为IPOL（International Journal of Computer Vision and Image Processing Online）文章。ASIFT作为一种增强的图像特征提取工具，其核心优势在于能够提高在实际应用中对仿射变化的鲁棒性和准确性，为图像处理领域的研究者和实践者提供了强大的技术支撑。

Guoshen Yu, Jean-Michel Morel

Figure 5: ASIFT algorithm overview.

u(x, y) → u(tx, y)). For digital images, the tilt is performed by a directional t-subsampling. It

therefore requires the previous application of an antialiasing ﬁlter in the direction of x, namely

the convolution by a Gaussian with standard deviation c

√

− 1. The value c = 0.8 is the

value shown [7] to ensure a very small aliasing error. These rotations and tilts are performed

for a ﬁnite and small number of latitude and longitude angles, the sampling steps of these

parameters ensuring that the simulated images keep close to any other possible view generated

by other values of φ and θ (see below).

2. All simulated images are compared by a similarity invariant matching algorithm (SIFT). SIFT

can be replaced by any other similarity invariant matching method. (There are many such

variants of SIFT). It is therefore not the object of this article to describe the SIFT method.

3. The SIFT method has its own wrong match elimination criterion. Nonetheless, it generally

leaves behind false matches, even in image pairs that do not correspond to the same scene.

ASIFT, by comparing many pairs, can therefore accumulate many wrong matches. It is im-

portant to ﬁlter out these matches. The criterion used is that the retained matches must be

compatible with an epipolar geometry. We use to that goal the ORSA method [5], which is

considered the most reliable method, robust to more outliers than a classic RANSAC proce-

dure. It is not the goal of this article to present ORSA. It is simply used to ﬁlter out the

matches given by both SIFT and ASIFT. Thus, it may occur that two images have no match

left at all. This does not necessarily mean that there are no ASIFT matches; the matches may

be all eliminated as incompatible with an epipolar geometry.

4.2 Parameter Sampling

The sampling precision of the latitude and longitude angles should increase with θ, since the image

distortion caused by a ﬁxed latitude or longitude angle displacement is more drastic at larger θ. As

described in Figure 6, the sampling of the latitude and longitude angles is speciﬁed below.

• The latitudes θ are sampled so that the associated tilts follow a geometric series 1, a, a

, . . . , a

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