Spatial relations between objects in an image have proved useful for structural object recognition. Structural constraints can act as regularization in neural network training, improving generalization capability with small datasets. Several relations can be modeled as a morphological dilation of a reference object with a structuring element representing the semantics of the relation, from which the degree of satisfaction of the relation between another object and the reference object can be derived. However, dilation is not differentiable, requiring an approximation to be used in the context of gradient-descent training of a network. We propose to approximate dilations using convolutions based on a kernel equal to the structuring element. We show that the proposed approximation, even if slightly less accurate than previous approximations, is definitely faster to compute and therefore more suitable for computationally intensive neural network applications.
翻译:图像中的物体之间的空间关系已证明对结构物体的识别有用。结构限制可以作为神经网络训练的正规化,用小数据集改进一般化能力。一些关系可以模拟为参考物体的形态变形,带有代表关系语义的构造要素,从中可以推断出另一个物体与参照对象之间关系的满意度。但是,变形是不可区别的,要求在网络的梯度-白化训练中使用近似值。我们提议使用与结构要素相等的内核来估计变形。我们表明,拟议的近似即使比先前的近似略低,也肯定更快地计算,因此更适合计算密集的神经网络应用。