图像拼接与PDF整合技术教程

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"图像拼接处理的教程，涵盖了图像对齐和拼接的算法，适合视频稳定、总结和全景图像创建等应用。" 在图像处理领域，图像拼接是一种技术，它将多张图片合并成一张大图，通常用于创建全景照片或在有限视角下展示更广阔的场景。这个过程主要涉及两个关键技术：图像对齐（Image Alignment）和图像拼接（Image Stitching）。图像对齐是图像拼接的基础，其目标是确定不同图像之间的对应关系，即使得重叠区域的像素能够正确匹配。这通常涉及到不同程度的重叠图像，如在视频稳定、视频摘要中，以及创建全景图像时。对齐算法可以基于像素级（pixel-based）或者特征级（feature-based）的方法。像素级方法直接比较图像的像素值，而特征级方法则识别图像中的显著点或结构，如边缘、角点，然后对这些特征进行匹配。特征级对齐算法通常更为鲁棒，因为它不那么依赖于精确的像素匹配。例如，SIFT（尺度不变特征变换）和SURF（加速稳健特征）就是常用的特征检测和描述算子，它们能够在光照变化、尺度变化等条件下保持稳定。图像拼接则是将对齐后的图像进行无缝融合，这需要解决由于视差、场景移动导致的模糊（blurring）和鬼影（ghosting）问题，以及因曝光差异引起的色彩不一致。融合算法通常会使用图像过渡技术，比如使用权重函数来平滑过渡区，减少视觉上的割裂感。此外，为了处理曝光差异，可能还需要进行色调映射（tonemapping）或亮度调整。该教程还讨论了基本的运动模型，这是理解对齐和拼接算法的关键。这些模型包括平移、旋转、缩放等基本几何变换，以及更复杂的仿射和透视变换。对于动态场景，可能还需要考虑时间相关的运动模型。最后，教程指出该领域的开放性研究问题，可能包括如何提高对齐精度、如何处理更大的视差、如何在复杂环境下（如快速移动物体、光照剧烈变化）实现更好的拼接效果，以及如何实现更加自然和无缝的图像融合。图像拼接处理是一个涉及多种技术和算法的复杂过程，它在摄影、虚拟现实、地图制作等多个领域都有广泛的应用。理解和掌握这些技术对于提升图像处理能力至关重要。

Figure 8: An example of a spherical panorama constructed from 54 photographs.

Professional panoramic photographers sometimes also use a pan-tilt head that makes it easy to

control the tilt and to stop at speciﬁc detents in the rotation angle. This not only ensures a uniform

coverage of the visual ﬁeld with a desired amount of image overlap, but also makes it possible

to stitch the images using cylindrical or spherical coordinates and pure translations. In this case,

pixel coordinates (x, y, f) must ﬁrst be rotated using the known tilt and panning angles before

being projected into cylindrical or spherical coordinates (Chen 1995). Having a roughly known

panning angle also makes it easier to compute the alignment, since the rough relative positioning

of all the input images is known ahead of time, enabling a reduced search range for alignment.

Figure 8 shows a full 3D rotational panorama unwrapped onto the surface of a sphere (Szeliski and

Shum 1997).

One ﬁnal coordinate mapping worth mentioning is the polar mapping where the north pole lies

along the optic axis rather than the vertical axis,

(cos θ sin φ, sin θ sin φ, cos φ) = s (x, y, z). (40)

In this case, the mapping equations become

′

= sφ cos θ = s

tan

−1

, (41)

′

= sφ sin θ = s

tan

−1

, (42)

where r =

√

+ y

is the radial distance in the (x, y) plane and sφ plays a similar role in the

′

, y

′

) plane. This mapping provides an attractive visualization surface for certain kinds of wide-

angle panoramas and is also a good model for the distortion induced by ﬁsheye lenses, as discussed

in §2.4. Note how for small values of (x, y), the mapping equations reduces to x

′

≈ sx/z, which

suggests that s plays a role similar to the focal length f.

mization to compute the alignment. Stein (1997) uses a feature-based approach combined with

a general 3D motion model (and quadratic radial distortion), which requires more matches than a

parallax-free rotational panorama but is potentially more general. More recent approaches some-

times simultaneously compute both the unknown intrinsic parameters and the radial distortion

coefﬁcients, which may include higher order terms or more complex rational or non-parametric

forms (Claus and Fitzgibbon 2005, Sturm 2005, Thirthala and Pollefeys 2005, Barreto and Dani-

ilidis 2005, Hartley and Kang 2005, Steele and Jaynes 2006, Tardif et al. 2006b).

Fisheye lenses require a different model than traditional polynomial models of radial distortion

(Figure 9c). Instead, ﬁsheye lenses behave, to a ﬁrst approximation, as equi-distance projectors

of angles away from the optic axis (Xiong and Turkowski 1997), which is the same as the polar

projection described by equations (40-42). Xiong and Turkowski (1997) describe how this model

can be extended with the addition of an extra quadratic correction in φ, and how the unknown

parameters (center of projection, scaling factor s, etc.) can be estimated from a set of overlapping

ﬁsheye images using a direct (intensity-based) non-linear minimization algorithm.

Even more general models of lens distortion exist. For example, one can represent any lens as

a mapping of pixel to rays in space (Gremban et al. 1988, Champleboux et al. 1992, Grossberg

and Nayar 2001, Tardif et al. 2006a), either represented as a dense mapping or using a sparser

interpolated smooth function such as a spline (Goshtasby 1989, Champleboux et al. 1992).

3 Direct (pixel-based) alignment

Once we have chosen a suitable motion model to describe the alignment between a pair of images,

we need to devise some method to estimate its parameters. One approach is to shift or warp the

images relative to each other and to look at how much the pixels agree. Approaches that use

pixel-to-pixel matching are often called direct methods, as opposed to the feature-based methods

described in the next section.

To use a direct method, a suitable error metric must ﬁrst be chosen to compare the images.

Once this has been established, a suitable search technique must be devised. The simplest tech-

nique is to exhaustively try all possible alignments, i.e., to do a full search. In practice, this may

be too slow, so hierarchical coarse-to-ﬁne techniques based on image pyramids have been devel-

oped. Alternatively, Fourier transforms can be used to speed up the computation. To get sub-pixel

precision in the alignment, incremental methods based on a Taylor series expansion of the image

function are often used. These can also be applied to parametric motion models. Each of these

techniques is described in more detail below.

3.1 Error metrics

The simplest way to establish an alignment between two images is to shift one image relative to

the other. Given a template image I

(x) sampled at discrete pixel locations {x

= (x

, y

)}, we

wish to ﬁnd where it is located in image I

(x). A least-squares solution to this problem is to ﬁnd

the minimum of the sum of squared differences (SSD) function

SSD

(u) =

+ u) − I

)]

, (44)

where u = (u, v) is the displacement and e

= I

+ u) − I

) is called the residual error

(or the displaced frame difference in the video coding literature).

(We ignore for the moment the

possibility that parts of I

may lie outside the boundaries of I

or be otherwise not visible.)

In general, the displacement u can be fractional, so a suitable interpolation function must be

applied to image I

(x). In practice, a bilinear interpolant is often used, but bi-cubic interpolation

should yield slightly better results. Color images can be processed by summing differences across

all three color channels, although it is also possible to ﬁrst transform the images into a different

color space or to only use the luminance (which is often done in video encoders).

Robust error metrics We can make the above error metric more robust to outliers by replacing

the squared error terms with a robust function ρ(e

) (Huber 1981, Hampel et al. 1986, Black and

Anandan 1996, Stewart 1999) to obtain

SRD

(u) =

ρ(I

+ u) − I

)) =

ρ(e

). (45)

The robust norm ρ(e) is a function that grows less quickly than the quadratic penalty associated

with least squares. One such function, sometimes used in motion estimation for video coding

because of its speed, is the sum of absolute differences (SAD) metric, i.e.,

SAD

(u) =

+ u) − I

)| =

|. (46)

However, since this function is not differentiable at the origin, it is not well suited to gradient-

descent approaches such as the ones presented in §3.4.

Instead, a smoothly varying function that is quadratic for small values but grows more slowly

away from the origin is often used. Black and Rangarajan (1996) discuss a variety of such func-

tions, including the Geman-McClure function,

(x) =

1 + x

, (47)

The usual justiﬁcation for using least squares is that it is the optimal estimate with respect to Gaussian noise. See

the discussion below on robust alternatives.

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