Abstract

AbstractExploring representations is a fundamental step towards understanding vision. The visual system carries two types of information along separate pathways: One is about what it is and the other is about where it is. Initially, the what is represented by a pattern of activity that is distributed across millions of photoreceptors, whereas the where is 'implicitly' given as their retinotopic positions. Many computational theories of object recognition rely on such pixel-based representations, but they are insufficient to learn spatial information such as position and size due to the implicit encoding of the where information. Here we try transforming a retinal image of an object into its internal image via interchanging the what with the where, which means that patterns of intensity in internal image describe the spatial information rather than the object information. To be concrete, the retinal image of an object is deformed and turned over into a negative image, in which light areas appear dark and vice versa, and the object's spatial information is quantified with levels of intensity on borders of that image. Interestingly, the inner part excluding the borders of the internal image shows the position and scale invariance. In order to further understand how the internal image associates the what and where, we examined the internal image of a face which moves or is scaled on the retina. As a result, we found that the internal images form a linear vector space under the object translation and scaling. In conclusion, these results show that the what-where interchangeability might play an important role for organizing those two into internal representation of brain.

Highlights

  • The inner parts of three conjugate images in the third column of figure 3 are the same and they are invariant to the position and scale

  • By assuming the soil as image intensity, the optimal mass transportation can be applied to automatic image morphing

  • Our formulation can be derived from the optimal transport theory: The optimal transportation from an image to the uniform intensity is the inverse transformation to the optimal transportation from its conjugate image to the uniform intensity, which is depicted in figure 1

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Summary

Introduction

The inner part of conjugate image explains how the scale invariance can be achieved. The position and scale information is incorporated into the intensity on the borders. The inner parts of three conjugate images in the third column of figure 3 are the same and they are invariant to the position and scale.

Results
Conclusion

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