Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an up-convolutional neural network. We apply the method to shallow representations (HOG, SIFT, LBP), as well as to deep networks. For shallow representations our approach provides significantly better reconstructions than existing methods, revealing that there is surprisingly rich information contained in these features. Inverting a deep network trained on ImageNet provides several insights into the properties of the feature representation learned by the network. Most strikingly, the colors and the rough contours of an image can be reconstructed from activations in higher network layers and even from the predicted class probabilities.
Mahendran and Vedaldi @cite_3 invert a differentiable image representation @math using gradient descent. Given a feature vector @math , they seek for an image @math which minimizes a loss function -- the squared Euclidean distance between @math and @math plus a regularizer enforcing a natural image prior. This method is fundamentally different from our approach in that it optimizes the difference between the feature vectors, not the image reconstruction error. Additionally, it includes a hand-designed natural image prior, while in our case the network implicitly learns such a prior. Technically, it involves optimization at test time, which requires computing the gradient of the feature representation and makes it relatively slow (the authors report 6s per image on a GPU). In contrast, the presented approach is only costly when training the inversion network. Reconstruction from a given feature vector just requires a single forward pass through the network, which takes roughly @math ms per image on a GPU. The method of @cite_3 requires gradients of the feature representation, therefore it could not be directly applied to non-differentiable representations such as LBP, or recordings from a real brain @cite_2 .
@cite_3 @cite_2
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Image representations, from SIFT and Bag of Visual Words to Convolutional Neural Networks (CNNs), are a crucial component of almost any image understanding system. Nevertheless, our understanding of them remains limited. In this paper we conduct a direct analysis of the visual information contained in representations by asking the following question: given an encoding of an image, to which extent is it possible to reconstruct the image itself? To answer this question we contribute a general framework to invert representations. We show that this method can invert representations such as HOG and SIFT more accurately than recent alternatives while being applicable to CNNs too. We then use this technique to study the inverse of recent state-of-the-art CNN image representations for the first time. Among our findings, we show that several layers in CNNs retain photographically accurate information about the image, with different degrees of geometric and photometric invariance. Summary Quantitative modeling of human brain activity can provide crucial insights about cortical representations [1, 2] and can form the basis for brain decoding devices [3–5]. Recent functional magnetic resonance imaging (fMRI) studies have modeled brain activity elicited by static visual patterns and have reconstructed these patterns from brain activity [6–8]. However, blood oxygen level-dependent (BOLD) signals measured via fMRI are very slow [9], so it has been difficult to model brain activity elicited by dynamic stimuli such as natural movies. Here we present a new motion-energy [10, 11] encoding model that largely overcomes this limitation. The model describes fast visual information and slow hemodynamics by separate components. We recorded BOLD signals in occipitotemporal visual cortex of human subjects who watched natural movies and fit the model separately to individual voxels. Visualization of the fit models reveals how early visual areas represent the information in movies. To demonstrate the power of our approach, we also constructed a Bayesian decoder [8] by combining estimated encoding models with a sampled natural movie prior. The decoder provides remarkable reconstructions of the viewed movies. These results demonstrate that dynamic brain activity measured under naturalistic conditions can be decoded using current fMRI technology.