This paper is devoted to a new paradigm for the invariant recognition of visual objects through introducing ‘the generating invariant’ of the underlying visual geometry which allows to numerically calculate differential signature curves in a fully group-invariant manner. Then, we utilize the results to work on the unsolved problem of approximating similarity differential invariant signatures based on suitable combination of joint invariants of the underlying group action. We also illustrate that, compared to the traditional and current schemes, the new paradigm is reliable, stable, significantly minimizes the effects of noise and indeterminacy, and Signature-inverse Theorem is correct in terms of it. Besides we demonstrate that the ratio of elapsed time and inaccuracy of the outcomes resulted from the Calabi et al.’s scheme to our formulation follow an exponential decay model. And finally, application to real images are discussed.

本文致力于通过引入底层视觉几何的“生成不变量”来实现视觉对象的不变识别的新范式，它允许以完全组不变的方式数值计算微分特征曲线。然后，我们利用这些结果来解决基于潜在组动作的联合不变量的适当组合来逼近相似性微分不变特征的未解决问题。我们还说明，与传统和当前方案相比，新范式可靠、稳定，显着减少了噪声和不确定性的影响，并且签名逆定理在这方面是正确的。此外，我们证明了 Calabi 等人导致的经过时间和结果不准确性的比率。我们公式的方案遵循指数衰减模型。最后，讨论了对真实图像的应用。