We consider the evolution model proposed in Bertalmío (Front Comput Neurosci 8:71, 2014), Bertalmío et al. (IEEE Trans Image Process 16(4):1058–1072, 2007) to describe illusory contrast perception phenomena induced by surrounding orientations. Firstly, we highlight its analogies and differences with the widely used Wilson–Cowan equations (Wilson and Cowan in BioPhys J 12(1):1–24, 1972), mainly in terms of efficient representation properties. Then, in order to explicitly encode local directional information, we exploit the model of the primary visual cortex (V1) proposed in Citti and Sarti (J Math Imaging Vis 24(3):307–326, 2006) and largely used over the last years for several image processing problems (Duits and Franken in Q Appl Math 68(2):255–292, 2010; Prandi and Gauthier in A semidiscrete version of the Petitot model as a plausible model for anthropomorphic image reconstruction and pattern recognition. SpringerBriefs in Mathematics, Springer, Cham, 2017; Franceschiello et al. in J Math Imaging Vis 60(1):94–108, 2018). The resulting model is thus defined in the space of positions and orientation, and it is capable of describing assimilation and contrast visual bias at the same time. We report several numerical tests showing the ability of the model to reproduce, in particular, orientation-dependent phenomena such as grating induction and a modified version of the Poggendorff illusion. For this latter example, we empirically show the existence of a set of threshold parameters differentiating from inpainting to perception-type reconstructions and describing long-range connectivity between different hypercolumns in V1.

我们考虑了Bertalmío（Front Comput Neurosci 8:71，2014），Bertalmío等人提出的进化模型。（IEEE Trans Image Process 16（4）：1058–1072，2007）描述了周围取向引起的虚幻对比度感知现象。首先，我们主要从有效表示特性方面着眼于与广泛使用的Wilson-Cowan方程（Wilson and Cowan in BioPhys J 12（1）：1-24，1972）的类比和差异。然后，为了显式编码本地方向信息，我们利用了Citti和Sarti（J Math Imaging Vis 24（3）：307-326，2006）中提出的主要视觉皮层（V1）的模型，并在最后年的几个图像处理问题（Duits和Franken在Q Appl Math 68（2）：255-292，2010; Prandi和Gauthier的Petitot模型的半离散版本，作为拟人化图像重建和模式识别的合理模型。施普林格数学简史，施普林格，湛，2017年; Franceschiello等。J Math Imaging Vis 60（1）：94–108，2018）。因此，在位置和方向的空间中定义了所得的模型，并且该模型能够同时描述同化和对比视觉偏差。我们报告了几个数值测试，这些测试表明了该模型能够再现的能力，尤其是与方向相关的现象，例如光栅感应和Poggendorff幻觉的修改版本。对于后一个示例，