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Title: FAST OBJECT LOCALIZATION VIA SENSITIVITY ANALYSIS

Paper content:
Deep Convolutional Neural Networks (CNNs) have been repeatedly shown to perform well on image classification tasks, successfully recognizing a broad array of objects when given sufficient training data.
Methods for object localization, however, are still in need of substantial improvement.
Common approaches to this problem involve the use of a sliding window, sometimes at multiple scales, providing input to a deep CNN trained to classify the contents of the window.
In general, these approaches are time consuming, requiring many classification calculations.
In this paper, we offer a fundamentally different approach to the localization of recognized objects in images.
Our method is predicated on the idea that a deep CNN capable of recognizing an object must implicitly contain knowledge about object location in its connection weights.
We provide a simple method to interpret classifier weights in the context of individual classified images.
This method involves the calculation of the derivative of network generated activation patterns, such as the activation of output class label units, with regard to each in- put pixel, performing a sensitivity analysis that identifies the pixels that, in a local sense, have the greatest influence on internal representations and object recognition.
These derivatives can be efficiently computed using a single backward pass through the deep CNN classifier, producing a sensitivity map of the image.
We demonstrate that a simple linear mapping can be learned from sensitivity maps to bounding box coordinates, localizing the recognized object.
Our experimental results, using real-world data sets for which ground truth localization information is known, reveal competitive accuracy from our fast technique.
Deep Convolutional Neural Networks (CNNs) have been shown to be effective at image classification, accurately performing object recognition even with thousands of object classes when trained on a sufficiently rich data set of labeled images BID14 .
One advantage of CNNs is their ability to learn complete functional mappings from image pixels to object categories, without any need for the extraction of hand-engineered image features BID21 .
To facilitate learning through stochastic gradient descent, CNNs are (at least approximately) differentiable with regard to connection weight parameters.Image classification, however, is only one of the problems of computer vision.
In the task of image classification, each image has a single label, associated with the class identity of the main object in the image, and the goal is to assign correct labels in a manner that generalizes to novel images.
This can be accomplished by training a machine learning classifier, such as a CNN, on a large data set of labeled images BID5 .
In the object localization task, in comparison, the output for a given image is not a class label but the locations of a specified number of objects in the image, usually encoded as bounding boxes.
Evaluation of an object localization system generally requires ground truth bounding boxes to compare to the system's output.
The detection task is more difficult than the localization task, as the number of objects are not predetermined BID21 .In
this paper, we focus on object localization, identifying the position in the image of a recognized object. As
is common in the localization literature, position information is output in the form of a bounding box. Previously
developed techniques for accomplishing this task generally involve searching the image for the object, considering many candidate bounding boxes with different sizes and locations, sometimes guided by an auxilliary algorithm for heuristically identifying regions of interest BID21 ; BID10 ; BID13 . For each candidate
location, the sub-image captured by the bounding box is classified for object category, with the final output Figure 1 : Examples of sensitivity maps, displaying the sensitivity of network internal representations to individual pixels, providing information about the locations of the main objects in the source images.bounding box either being the specific candidate region classified as the target object with the highest level of certainty or some heuristic combination of neighboring or overlapping candidate regions with high classification certainty. These approaches tend
to be time consuming, often requiring deep CNN classification calculations of many candidate regions at multiple scales. Efforts to speed these
methods mostly focus on reducing the number of regions considered, typically by using some adjunct heuristic region proposal algorithm BID10 ; BID17 ; BID13 . Still, the number of considered
regions is often reported to be roughly 2,000 per image. While these approaches can be fairly
accurate, their slowness limits their usefulness, particularly for online applications.A noteworthy alternative approach is to directly train a deep CNN to produce outputs that match ground truth localization bounding boxes, using a large image data set that provides both category and localization information for each image. It appears as if some form of this method
was used with AlexNet BID14 , though details concerning localization, rather than image classification, are difficult to discern from the published literature. A natural approach would be to cast the learning
of bounding boxes as a simple regression problem, with targets being the four coordinates that specify a bounding box (e.g., coordinates of upper-left and lower-right corners, or region center coordinates along with region width and height). It is reasonable to consider sharing early layers
of a deep CNN, such as those performing convolution and max pooling, between both an image classification network and an object localization network. Indeed, taking such a multitask learning approach
BID2 can allow for both object category and object location training data to shape connection weights throughout the network. Thus, the deep CNN would have "two heads", one for
image classification, using a classification cross-entropy loss function, and one for object localization, reducing the 2 norm between ground truth and predicted bounding box coordinates BID14 . While this approach can produce a network that quickly
outputs location information, extensive training on large data sets containing ground truth bounding box information is necessary to produce good generalization.In this paper, we introduce an approach to object localization that is both very fast and robust in the face of limited ground truth bounding box training data. This approach is rooted in the assertion that any deep
CNN for image classification must contain, implicit in its connection weights, knowledge about the location of recognized objects BID20 . The goal, then, is to interpret the flow of activation
in an object recognition network when it is performing image classification so as to extract information about object location. Furthermore, the goal is to do this quickly. Thus, this
approach aims to leverage location knowledge
that is already latent in extensively trained and tuned image classification networks, without requiring a separate learning process for localization.Our method makes use of the notion of a sensitivity analysis BID26 . We propose estimating the sensitivity of the category outputs
, or activation patterns at internal network layers, of an image classification CNN to variance in each input pixel, given a specific input image. The result is a numeric value for each pixel in the input image
that captures the degree to which small changes in that pixel (locally, around its current value) give rise to large changes in the output category. Together, these numeric values form a sensitivity map of the image
, encoding image regions that are important for the current classification. Our proposed measure of sensitivity is the partial derivative of
activity with regard to each pixel value, evaluated for the current image. For a deep CNN that formally embodies a differentiable mapping (
at least approximately) from image pixels to output categories, this partial derivative can be quickly calculated. While many tools currently exist for efficiently calculating such
derivatives, we provide a simple algorithm that computes these values through a single backward pass through the image classification network, similar to that used to calculate unit error (delta) values in the backpropagation of error learning algorithm BID18 . Thus, we can generate a sensitivity map for an image in about the
same amount of time as it takes the employed image classification network to produce an output. Some example sensitivity maps are shown in Figure 1 .The idea of
using sensitivity information, like that in our sensitivity
maps, for a variety of tasks, including localization, has previously appeared in the literature BID24 ; BID28 BID20 . Indeed, some of these past efforts have used more sophisticated measures
of sensitivity. In this paper, we show that even our very simple sensitivity measure can
produce strong localization performance, and it can do so quickly, without any modifications to the classification network, and even for object categories on which the classification network was not trained. The relationship of the results reported here to previously reported work
is discussed further in Section 4.As previously mentioned, object localization methods typically encode object location as a bounding box. Since our sensitivity maps encode location differently, in terms of pixels
, we propose learning a simple linear mapping from sensitivity maps to bounding box coordinates, allowing our method to output a bounding box for each classified image. We suggest that this linear mapping can be robustly learned from a relatively
small training set of images with ground truth bounding boxes, since the sensitivity maps form a much more simple input than the original images.The primary contributions of this paper may be summarized as follows:• We propose a new general approach to performing object localization, interpreting a previously trained image classification network by performing a sensitivity analysis, identifying pixels to which the category output, or a more general internal representation, is particularly sensitive.• We demonstrate how a linear function from the resulting sensitivity maps to
object location bounding box coordinates may be learned from training images containing ground truth location information.• We provide a preliminary assessment of our approach, measuring object localization
performance on the ImageNet and PASCAL VOC data sets using the VGG16 image classification CNN, showing strong accuracy while maintaining short computation times.
We have presented an approach to object localization based on performing a sensitivity analysis of a previously trained image classification deep CNN.
Our method is fast enough to be used in online applications, and it demonstrates accuracy that is superior to some methods that are much slower.
It is likely that even better accuracy could be had by incorporating sensitivity analysis information into a more sophisticated bounding box estimator.As previously noted, the idea of using sensitivity information has appeared in previously published work.
There are ways in which the results reported in this paper are distinct, however.
We have moved beyond visualization of network function using sensitivity (or saliency) BID24 to performing direct comparisons between different methods on the localization task.
We have shown that using a fast and simple measure of sensitivity can produce comparable performance to that of much slower methods.
Our approach produces good generalization without modifying the classification network, as is done in Class Activation Mapping (CAM) BID28 .
With our PASCAL VOC 2007 results, we have shown that our approach can successfully be applied to attention maps, even when the image contains objects belonging to a class on which the classification network was not trained, distinguishing it from Grad-CAM Selvaraju et al. (2016) .
In short, we have demonstrated the power of a simple sensitivity measure for performing localization.Note that our approach may be used with image classifiers other than CNNs.
The proposed sensitivity analysis can be conducted on any differentiable classifier, though performance will likely depend on classifer specifics.
Indeed, at a substantial time cost, even a black box classifier could be approximately analyzed by making small changes to pixels and observing the effects on activation patterns.The proposed approach is quite general.
Indeed, we are currently working on applying sensitivity analysis to deep networks trained on other tasks, with the goal of interpreting network performance on the current input in a useful way.
Thus, we see a potentially large range of uses for sensitivity analysis in neural network applications.

assistant: text: Proposing a novel object localization(detection) approach based on interpreting the deep CNN using internal representation and network's thoughts