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首页> 外文会议>European Conference on Computer Vision(ECCV 2004) pt.4; 20040511-20040514; Prague; CZ >Support Blob Machines The Sparsification of Linear Scale Space
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Support Blob Machines The Sparsification of Linear Scale Space

机译：支持Blob机线性尺度空间的稀疏化

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摘要

A novel generalization of linear scale space is presented. The generalization allows for a sparse approximation of the function at a certain scale. To start with, we first consider the Tikhonov regularization viewpoint on scale space theory. The sparsification is then obtained using ideas from support vector machines and based on the link between sparse approximation and support vector regression as described in [4] and [19]. In regularization theory, an ill-posed problem is solved by searching for a solution having a certain differentiability while in some precise sense the final solution is close to the initial signal. To obtain scale space, a quadratic loss function is used to measure the closeness of the initial function to its scale σ image. We propose to alter this loss function thus obtaining our generalization of linear scale space. Comparable to the linear ε-insensitive loss function introduced in support vector regression, we use a quadratic ε-insensitive loss function instead of the original quadratic measure. The ε-insensitivity loss allows errors in the approximating function without actual increase in loss. It penalizes errors only when they become larger than the a priory specified constant ε. The quadratic form is mainly maintained for consistency with linear scale space. Although the main concern of the article is the theoretical connection between the foregoing theories, the proposed approach is tested and exemplified in a small experiment on a single image.
机译：提出了线性尺度空间的一种新颖的概括。泛化允许在一定规模上对函数进行稀疏近似。首先，我们首先考虑尺度空间理论的Tikhonov正则化观点。然后使用支持向量机的思想并基于稀疏近似和支持向量回归之间的联系来获得稀疏性，如[4]和[19]中所述。在正则化理论中，不适定问题是通过寻找具有一定可微性的解来解决的，而在某种意义上，最终解接近于初始信号。为了获得标度空间，使用二次损失函数来测量初始函数与其标度σ图像的接近度。我们建议更改此损失函数，从而获得线性尺度空间的一般化。与支持向量回归中引入的线性ε不敏感损失函数相比，我们使用二次ε不敏感损失函数代替了原始的二次度量。 ε不灵敏性损失允许近似函数出现错误，而实际损失并未增加。仅当误差大于先前指定的常数ε时，才会对误差进行惩罚。保持二次形式主要是为了与线性标度空间保持一致。虽然本文的主要关注点是上述理论之间的理论联系，但是在单个图像的小型实验中对提出的方法进行了测试和举例说明。

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