图像拼接--A multiresolution spline with application to image mosaics

A multiresolution spline with application to image mosaics 《Acm Trans on Graphics》 , 1983 , 2 (4) :217-236

本文主要介绍使用 Multiresolution Spline算法来消除图像拼接之间的痕迹 A technical problem common to all applications of photomosaics is joining two images so that the edge between them is not visible 如下图所示：两个图像拼接线中间有一个明显痕迹

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首先介绍了一下要解决的问题

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这里使用 image spline 来表示消除痕迹的手段 We will use the term image spline to refer to digital techniques for making these adjustments.

这里我们先描述一个简化版本的问题，一维信号拼接 这里我们介绍 a weighted average splining technique.

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在拼接的邻域乘以一个权重系数，然后叠加两个图像（sum），这个算法的关键是 T 宽度的选择，宽度太小 消除痕迹不明显，仍有痕迹残留，宽度太大，会将边界附近的边缘特征削弱 If T is small compared to image features, then the boundary may still appear as a step in image gray level, albeit a somewhat blurred step. 宽度过大会造成一个物体重影，类似双曝光现象 If, on the other hand, T is large compared to image features, features from both images may appear superimposed within the transition zone, as in a photographic double exposure.

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Clearly, the size of the transition zone, relative to the size of image features, plays a critical role in image splining 所以这个宽度的选择和图像特征尺寸大小密切相关。

To eliminate a visible edge the transition width should be at least comparable in size to the largest prominent features in the image. On the other hand, to avoid a double exposure effect, the zone should not be much larger than the smallest prominent image features. There is no choice of T which satisfies both requirements in the star images of Figure 3 because these contain both a diffuse background and small bright stars.

上面的两难问题我们可以换一种方式表达：image spatial frequency content. In particular, a suitable T can only be selected if the images to be splined occupy a relatively narrow spatial frequency band.

如果图像只分高频信息和低频信息，那么在高频信息中我们使用较小的 T，在低频信息中选择较大 T

The approach proposed here is that such images should first be decomposed into a set of band-pass component images. A separate spline with an appropriately selected T can then be performed in each band. Finally, the splined band-pass components are recombined into the desired mosaic image. We call this approach the multiresolution spline. 这里我们将图像分解为多个 band-pass component images，在每个 band 中进行拼接，最后叠加所有 components

以上就是 multiresolution spline 大致思路。

下面是算法实现的具体细节 2. Basic Pyramid Operations A sequence of low-pass filtered images Go, G1 … , GN can be obtained by repeatedly convolving a small weighting function with an image

Convolution with a Gaussian has the effect of low-pass filtering the image. Pyramid construction is equivalent to convolving the image with a set of Gaussian-like functions to produce a corresponding set of filtered images. Because of the importance of the multiple filter interpretation, we shall refer to this sequence of images Go,G1 … GN as the Gaussian pyramid.

The Gaussian pyramid is a set of low-pass filtered images. In order to obtain the band-pass images required for the multiresolution spline we subtract each level of the pyramid from the next lowest level.

This difference of Gaussian-like functions resembles the Laplacian operators commonly used in the image processing [5], so we refer to the sequence Lo, L1 … , LN as the Laplacian pyramid.

multiresolution spline algorithm:

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The idea behind multi-band blending is to blend low frequencies over a large spatial range, and high frequencies over a short range.