Summary
CNNs, as well as classic computer vision features (e.g., SIFT, HOG), extracts some form of representations from images. In terms of SIFT, it’s the SIFT key points. In terms of CNN, it’s the activation maps of different layers. This paper tries to reconstruct the original image from these representations (i.e., inverting the transformation). Such reconstruction provides insight into what the algorithm is looking for in an image.
Formulating reconstruction as a gradient-descent-able optimization problem
The paper formulates the reconstruction problem as an end-to-end optimization problem. It adjusts the pixel values of the reconstructed image (x) to minimize an objective function.
Expected, the objective function is
(loss = l_2 distance of representation) + (regularization = natural image prior)
Usually, there are more than one “good” reconstructed images due to the non-convexity of the problem. It initializes the input with different seeds to obtain different samples.
This formulation treats the algorithm (CNN, SIFT, HOG) mostly as a black box. The only requirement is that the transformation needs to be differentiable, so that it can use gradient descent.
Implementing SIFT and HOG as DNN
The paper describes how we can implement SIFT and HOG in the form of DNN so that they become differentiable, amenable to gradient descent. Refer to the paper for details.
Observations
CNN
Reconstruction from early layers in CNN yields images that look photometrically similar to the original image.
Reconstruction from higher layers in CNN yields images that repeat “import parts” of the object or composite them in a different way.
Reconstructing from a smaller spatial region
The natural image prior drives the input pixels that reside outside the receptive field of the selected region to become “blank”.
Reconstructing from a subset of channels
Inverting a subset of channels from AlexNet shows some channels focus on shape while other focus on color. The same observation was also reported in the original AlexNet paper.