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Title: Image Segmentation by Iterative Inference from Conditional Score Estimation

Paper content:
Inspired by the combination of feedforward and iterative computations in the visual cortex, and taking advantage of the ability of denoising autoencoders to estimate the score of a joint distribution, we propose a novel approach to iterative inference for capturing and exploiting the complex joint distribution of output variables conditioned on some input variables.
This approach is applied to image pixel-wise segmentation, with the estimated conditional score used to perform gradient ascent towards a mode of the estimated conditional distribution.
This extends previous work on score estimation by denoising autoencoders to the case of a conditional distribution, with a novel use of a corrupted feedforward predictor replacing Gaussian corruption.
An advantage of this approach over more classical ways to perform iterative inference for structured outputs, like conditional random fields (CRFs), is that it is not any more necessary to define an explicit energy function linking the output variables.
To keep computations tractable, such energy function parametrizations are typically fairly constrained, involving only a few neighbors of each of the output variables in each clique.
We experimentally find that the proposed iterative inference from conditional score estimation by conditional denoising autoencoders performs better than comparable models based on CRFs or those not using any explicit modeling of the conditional joint distribution of outputs.
Based on response timing and propagation delays in the brain, a plausible hypothesis is that the visual cortex can perform fast feedforward BID21 inference when an answer is needed quickly and the image interpretation is easy enough (requiring as little as 200ms of cortical propagation for some object recognition tasks, i.e., just enough time for a single feedforward pass) but needs more time and iterative inference in the case of more complex inputs BID23 .
Recent deep learning research and the success of residual networks BID9 BID8 point towards a similar scenario BID16 : early computation which is feedforward, a series of non-linear transformations which map low-level features to high-level ones, while later computation is iterative (using lateral and feedback connections in the brain) in order to capture complex dependencies between different elements of the interpretation.
Indeed, whereas a purely feedforward network could model a unimodal posterior distribution (e.g., the expected target with some uncertainty around it), the joint conditional distribution of output variables given inputs could be more complex and multimodal.
Iterative inference could then be used to either sample from this joint distribution or converge towards a dominant mode of that distribution, whereas a unimodaloutput feedfoward network would converge to some statistic like the conditional expectation, which might not correspond to a coherent configuration of the output variables when the actual conditional distribution is multimodal.This paper proposes such an approach combining a first feedforward phase with a second iterative phase corresponding to searching for a dominant mode of the conditional distribution while tackling the problem of semantic image segmentation.
We take advantage of theoretical results BID0 on denoising autoencoder (DAE), which show that they can estimate the score or negative gradient of the energy function of the joint distribution of observed variables: the difference between the reconstruction and the input points in the direction of that estimated gradient.
We propose to condition the autoencoder with an additional input so as to obtain the conditional score, Given an input image x, we extract a segmentation candidate y and intermediate feature maps h by applying a pre-trained segmentation network.
We add some noise to y and train a DAE that takes as input both y and h by minimizing Eq. 3. Training scenario 1
(a) yields the best results and uses the corrupted prediction as input to the DAE during training.
Training scenario 2
(b) corresponds to the original DAE prescription in the conditional case, and uses a corruption of the ground truth as input to the DAE during training.i.e., the gradient of the energy of the conditional density of the output variables, given the input variables.
The autoencoder takes a candidate output y as well as an input x and outputs a valueŷ so thatŷ − y estimates the direction DISPLAYFORM0 .
We can then take a gradient step in that direction and update y towards a lower-energy value and iterate in order to approach a mode of the implicit p(y|x) captured by the autoencoder.
We find that instead of corrupting the segmentation target as input of the DAE, we obtain better results by training the DAE with the corrupted feedforward prediction, which is closer to what will be seen as the initial state of the iterative inference process.
The use of a denoising autoencoder framework to estimate the gradient of the energy is an alternative to more traditional graphical modeling approaches, e.g., with conditional random fields (CRFs) BID14 BID10 , which have been used to model the joint distribution of pixel labels given an image BID13 .
The potential advantage of the DAE approach is that it is not necessary to decide on an explicitly parametrized energy function: such energy functions tend to only capture local interactions between neighboring pixels, whereas a convolutional DAE can potentially capture dependencies of any order and across the whole image, taking advantage of the state-of-the-art in deep convolutional architectures in order to model these dependencies via the direct estimation of the energy function gradient.
Note that this is different from the use of convolutional networks for the feedforward part of the network, and regards the modeling of the conditional joint distribution of output pixel labels, given image features.The main contributions of this paper are the following: 1. A novel training framework for modeling structured output conditional distributions, which is an alternative to CRFs, inspired by denoising autoencoder estimation of energy gradients.
2. Showing how this framework can be used in an architecture for image pixel-wise segmentation, in which the above energy gradient estimator is used to propose a highly probable segmentation through gradient descent in the output space.
3. Demonstrating that this approach to image segmentation outperforms or matches classical alternatives such as combining convolutional nets with CRFs and more recent state-of-theart alternatives on the CamVid dataset.
We have proposed to use a novel form of denoising autoencoders for iterative inference in structured output tasks such as image segmentation.
The autoencoder is trained to map corrupted predictions to target outputs and iterative inference interprets the difference between the output and the input as a direction of improved output configuration, given the input image.Experiments provide positive evidence for the three questions raised at the beginning of Sec. 4: (1) a conditional DAE can be used successfully as the building block of iterative inference for image segmentation, (2) the proposed corruption model (based on the feedforward prediction) works better than the prescribed target output corruption, and (3) the resulting segmentation system outperforms state-of-the-art methods for obtaining coherent outputs.

assistant: text: Refining segmentation proposals by performing iterative inference with conditional denoising autoencoders.