Predicting Identity-Preserving Object Transformations across the Human Ventral Visual Stream

Inferring shape transformations in a drawing task

Many objects and materials in our environment are subject to transformations that alter their shape. For example, branches bend in the wind, ice melts, and paper crumples. Still, we recognize objects and materials across these changes, suggesting we can distinguish an object's original features from those caused by the transformations ("shape scission"). Yet, if we truly understand transformations, we should not only be able to identify their signatures but also actively apply the transformations to new objects (i.e., through imagination or mental simulation). Here, we investigated this ability using a drawing task. On a tablet computer, participants viewed a sample contour and its transformed version, and were asked to apply the same transformation to a test contour by drawing what the transformed test shape should look like. Thus, they had to (i) infer the transformation from the shape differences, (ii) envisage its application to the test shape, and (iii) draw the result. Our findings show that drawings were more similar to the ground truth transformed test shape than to the original test shape-demonstrating the inference and reproduction of transformations from observation. However, this was only observed for relatively simple shapes. The ability was also modulated by transformation type and magnitude but not by the similarity between sample and test shapes. Together, our findings suggest that we can distinguish between representations of original object shapes and their transformations, and can use visual imagery to mentally apply nonrigid transformations to observed objects, showing how we not only perceive but also 'understand' shape.

Toward a computational theory of manifold untangling: from global embedding to local flattening

It has been hypothesized that the ventral stream processing for object recognition is based on a mechanism called cortically local subspace untangling. A mathematical abstraction of object recognition by the visual cortex is how to untangle the manifolds associated with different object categories. Such a manifold untangling problem is closely related to the celebrated kernel trick in metric space. In this paper, we conjecture that there is a more general solution to manifold untangling in the topological space without artificially defining any distance metric. Geometrically, we can either embed a manifold in a higher-dimensional space to promote selectivity or flatten a manifold to promote tolerance. General strategies of both global manifold embedding and local manifold flattening are presented and connected with existing work on the untangling of image, audio, and language data. We also discuss the implications of untangling the manifold into motor control and internal representations.

Predicting Identity-Preserving Object Transformations in Human Posterior Parietal Cortex and Convolutional Neural Networks

Previous research shows that, within human occipito-temporal cortex (OTC), we can use a general linear mapping function to link visual object responses across nonidentity feature changes, including Euclidean features (e.g., position and size) and non-Euclidean features (e.g., image statistics and spatial frequency). Although the learned mapping is capable of predicting responses of objects not included in training, these predictions are better for categories included than those not included in training. These findings demonstrate a near-orthogonal representation of object identity and nonidentity features throughout human OTC. Here, we extended these findings to examine the mapping across both Euclidean and non-Euclidean feature changes in human posterior parietal cortex (PPC), including functionally defined regions in inferior and superior intraparietal sulcus. We additionally examined responses in five convolutional neural networks (CNNs) pretrained with object classification, as CNNs are considered as the current best model of the primate ventral visual system. We separately compared results from PPC and CNNs with those of OTC. We found that a linear mapping function could successfully link object responses in different states of nonidentity transformations in human PPC and CNNs for both Euclidean and non-Euclidean features. Overall, we found that object identity and nonidentity features are represented in a near-orthogonal, rather than complete-orthogonal, manner in PPC and CNNs, just like they do in OTC. Meanwhile, some differences existed among OTC, PPC, and CNNs. These results demonstrate the similarities and differences in how visual object information across an identity-preserving image transformation may be represented in OTC, PPC, and CNNs.