This work presents a contrast enhancement operator based on a fuzzy-numerical description of images at the pixel level; this operator is further used to construct a scale-space, whose theoretical and practical properties are reviewed. A very remarkable feature of our scale-space is that, in contrast to many other scale-spaces, it converges to non-trivial stages. Within the study of our scale-space, we present a series of theoretical results that show that the convergence of the scale-space is closely related to the signal's convexity. Specifically, we prove formally that the intensities in convex signals tend to converge to the minimum intensity. As a result, our scale-space increases the contrast in the image and homogenizes images. In addition to theoretical results, we illustrate the scale-space's behaviour in ad-hoc 1D signals and in greyscale images. Finally, to validate the potential application of this theoretical approach, we show that the proposal can be used as a preprocessing that performed before a neural network technique, increasing the accuracy in a classification task.

这项工作提出了一种基于像素级图像模糊数值描述的对比度增强算子；该算子进一步用于构建尺度空间，对其理论和实践性质进行了回顾。我们的尺度空间的一个非常显着的特征是，与许多其他尺度空间相比，它收敛到非平凡的阶段。在对尺度空间的研究中，我们提出了一系列理论结果，表明尺度空间的收敛与信号的凸度密切相关。具体来说，我们正式证明凸信号的强度趋于收敛到最小强度。结果，我们的尺度空间增加了图像的对比度并使图像均匀化。除了理论结果，我们还说明了尺度空间'一维信号和灰度图像。最后，为了验证这种理论方法的潜在应用，我们表明该提议可以用作在神经网络技术之前执行的预处理，从而提高分类任务的准确性。