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Archive for the ‘Machine Learning’ Category

Generative Adversarial Nets: Your Enemy is Your Best Friend?

In Computer Vision, deep learning, Machine Learning, Paper Talk on March 20, 2017 at 7:10 pm

by Li Yang Ku (gooly)

Generating realistic images with machines was always one of the top items on my list of difficult tasks. Past attempts in the Computer Vision community were only able to get a blurry image at best. The well publicized Google Deepdream project was able to generate some interesting artsy images, however they were modified from existing images and were designed more to make you feel like on drugs then realistic. Recently (2016), a work that combines the generative adversarial network framework with convolutional neural networks (CNNs) generated some results that look surprisingly good. (A non vision person would likely not be amazed though.) This approach was quickly accepted by the community and was referenced more then 200 times in less then a year.

This work is based on an interesting concept first introduced by Goodfellow et al. in the paper “Generative Adversarial Nets” at NIPS 2014 (http://papers.nips.cc/paper/5423-generative-adversarial-nets). The idea was to have two neural networks compete with each other. One would try to generate images as realistic as it can and the other network would try to distinguish them from real images at its best. By theory this competition will reach a global optimum where the generated image and the real image will belong to the same distribution (Could be a lot trickier in practice though). This work in 2014 got some pretty good results on digits and faces but the generated natural images are still quite blurry (see figure above).

In the more recent work “Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks” by Radford, Metz, and Chintala, convolutional neural networks and the generative adversarial net framework are successfully combined with a few techniques that help stabilize the training (https://arxiv.org/abs/1511.06434). Through this approach, the generated images are sharp and surprisingly realistic at first glance. The figures above are some of the generated bedroom images. Notice that if you look closer some of them may be weird.

The authors further explored what the latent variables represents. Ideally the generator (neural network that generates image) should disentangle independent features and each latent variable should represent a meaningful concept. By modifying these variables, images that have different characteristics can be generated. Note that these latent variables are what given to the neural network that generates images and is randomly sampled from a uniform distribution in the previous examples. In the figure above is an example where the authors show that the latent variables do represent meaningful concepts through arithmetic operations. If you subtract the average latent variables of men without glasses from the average latent variables of men with glasses and add the average latent variables of women without glasses, you obtain a latent variable that result in women with glasses when passed through the generator. This process identifies the latent variables that represent glasses.

 

 

 

Convolutional Neural Network Features for Robot Manipulation

In Computer Vision, deep learning, Robotics on October 24, 2016 at 6:30 am

by Li Yang Ku (Gooly)

bender_turtle

In my previous post, I mentioned the obstacles when applying deep learning techniques directly to robotics. First, training data is harder to acquire; Second, interacting with the world is not just a classification problem. In this post, I am gonna talk about a really simple approach that treats convolutional neural networks (CNNs) as a feature extractor that generates a set of features similar to traditional features such as SIFT. This idea is applied to grasping on Robonaut 2 and published in arXiv (Associating Grasp Configurations with Hierarchical Features in Convolutional Neural Networks) with more details. The ROS package called ros-deep-vision that generates such features using a RGB-D sensor is also public.

Hierarchical CNN Features

 

When we look at these deep models such as CNNs, we should keep in mind that these models work well because how the layers stack up hierarchically matches how the data is structured. Our observed world is also hierarchical, there are common shared structures such as edges that can be used to represent more complex structures such as squares and cubes when combined in meaningful ways. A simple view of CNN is just a tree structure, where a higher level neuron is a combination of neurons in the previous layer. For example, a neuron that represents cuboids is a combination of neurons that represent the corners and edges of the cuboid. The figures above show such examples on neurons that found to activate consistently on cuboids and cylinders.

Deep Learning for Robotics

By taking advantage of this hierarchical nature of CNN, we can turn a CNN into a feature extractor that generates features that represents local structures of a higher level structure. For example, such hierarchical features can represent the left edge of the top face of a box while traditional edge detectors would find all edges in the scene. Instead of representing a feature with a single filter (neuron) in one of the CNN layers, this feature, which we call hierarchical CNN feature, uses a tuple of filters from different layers. Using backpropagation that restricts activation to one filter per layer allows us to locate the location of such feature precisely. By finding features such as the front and back edge of the top face of a box we can learn where to place robot fingers relative to these hierarchical CNN features in order to manipulate the object.

robonaut 2 grasping

 

The most cited papers in computer vision and deep learning

In Computer Vision, deep learning, Paper Talk on June 19, 2016 at 1:18 pm

by Li Yang Ku (Gooly)

paper citation

In 2012 I started a list on the most cited papers in the field of computer vision. I try to keep the list focus on researches that relate to understanding this visual world and avoid image processing, survey, and pure statistic works. However, the computer vision world have changed a lot since 2012 when deep learning techniques started a trend in the field and outperformed traditional approaches on many computer vision benchmarks. No matter if this trend on deep learning lasts long or not I think these techniques deserve their own list.

As I mentioned in the previous post, it’s not always the case that a paper cited more contributes more to the field. However, a highly cited paper usually indicates that something interesting have been discovered. The following are the papers to my knowledge being cited the most in Computer Vision and Deep Learning (note that it is “and” not “or”). If you want a certain paper listed here, just comment below.

Cited by 5518

Imagenet classification with deep convolutional neural networks

A Krizhevsky, I Sutskever, GE Hinton, 2012

Cited by 1868

Caffe: Convolutional architecture for fast feature embedding

Y Jia, E Shelhamer, J Donahue, S Karayev…, 2014

Cited by 1681

Backpropagation applied to handwritten zip code recognition

Y LeCun, B Boser, JS Denker, D Henderson…, 1989

Cited by 1516

Rich feature hierarchies for accurate object detection and semantic segmentation

R Girshick, J Donahue, T Darrell…, 2014

Cited by 1405

Very deep convolutional networks for large-scale image recognition

K Simonyan, A Zisserman, 2014

Cited by 1169

Improving neural networks by preventing co-adaptation of feature detectors

GE Hinton, N Srivastava, A Krizhevsky…, 2012

Cited by 1160

Going deeper with convolutions

C Szegedy, W Liu, Y Jia, P Sermanet…, 2015

Cited by 977

Handwritten digit recognition with a back-propagation network

BB Le Cun, JS Denker, D Henderson…, 1990

Cited by 907

Visualizing and understanding convolutional networks

MD Zeiler, R Fergus, 2014

Cited by 839

Dropout: a simple way to prevent neural networks from overfitting

N Srivastava, GE Hinton, A Krizhevsky…, 2014

Cited by 839

Overfeat: Integrated recognition, localization and detection using convolutional networks

P Sermanet, D Eigen, X Zhang, M Mathieu…, 2013

Cited by 818

Learning multiple layers of features from tiny images

A Krizhevsky, G Hinton, 2009

Cited by 718

DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition

J Donahue, Y Jia, O Vinyals, J Hoffman, N Zhang…, 2014

Cited by 691

Deepface: Closing the gap to human-level performance in face verification

Y Taigman, M Yang, MA Ranzato…, 2014

Cited by 679

Deep Boltzmann Machines

R Salakhutdinov, GE Hinton, 2009

Cited by 670

Convolutional networks for images, speech, and time series

Y LeCun, Y Bengio, 1995

Cited by 570

CNN features off-the-shelf: an astounding baseline for recognition

A Sharif Razavian, H Azizpour, J Sullivan…, 2014

Cited by 549

Learning hierarchical features for scene labeling

C Farabet, C Couprie, L Najman…, 2013

Cited by 510

Fully convolutional networks for semantic segmentation

J Long, E Shelhamer, T Darrell, 2015

Cited by 469

Maxout networks

IJ Goodfellow, D Warde-Farley, M Mirza, AC Courville…, 2013

Cited by 453

Return of the devil in the details: Delving deep into convolutional nets

K Chatfield, K Simonyan, A Vedaldi…, 2014

Cited by 445

Large-scale video classification with convolutional neural networks

A Karpathy, G Toderici, S Shetty, T Leung…, 2014

Cited by 347

Deep visual-semantic alignments for generating image descriptions

A Karpathy, L Fei-Fei, 2015

Cited by 342

Delving deep into rectifiers: Surpassing human-level performance on imagenet classification

K He, X Zhang, S Ren, J Sun, 2015

Cited by 334

Learning and transferring mid-level image representations using convolutional neural networks

M Oquab, L Bottou, I Laptev, J Sivic, 2014

Cited by 333

Convolutional networks and applications in vision

Y LeCun, K Kavukcuoglu, C Farabet, 2010

Cited by 332

Learning deep features for scene recognition using places database

B Zhou, A Lapedriza, J Xiao, A Torralba…,2014

Cited by 299

Spatial pyramid pooling in deep convolutional networks for visual recognition

K He, X Zhang, S Ren, J Sun, 2014

Cited by 268

Long-term recurrent convolutional networks for visual recognition and description

J Donahue, L Anne Hendricks…, 2015

Cited by 261

Two-stream convolutional networks for action recognition in videos

K Simonyan, A Zisserman, 2014

 

Convolutional Neural Networks in Robotics

In Computer Vision, deep learning, Machine Learning, Neural Science, Robotics on April 10, 2016 at 1:29 pm

by Li Yang Ku (Gooly)

robot using tools

As I mentioned in my previous post, Deep Learning and Convolutional Neural Networks (CNNs) have gained a lot of attention in the field of computer vision and outperformed other algorithms on many benchmarks. However, applying these technics to robotics is non-trivial for two reasons. First, training large neural networks requires a lot of training data and collecting them on robots is hard. Not only do research robots easily have network or hardware failures after many trials, the time and resource needed to collect millions of data is also significant. The trained neural network is also robot specific and cannot be used on a different type of robot directly, therefore limiting the incentive of training such network. Second, CNNs are good for classification but when we are talking about interacting with a dynamic environment there is no direct relationship. Knowing you are seeing a lightsaber gives no indication on how to interact with it. Of course you can hard code this information, but that would just be using Deep Learning in computer vision instead of robotics.

Despite these difficulties, a few groups did make it through and successfully applied Deep Learning and CNNs in robotics; I will talk about three of these interesting works.

  • Levine, Sergey, et al. “End-to-end training of deep visuomotor policies.” arXiv preprint arXiv:1504.00702 (2015). 
  • Finn, Chelsea, et al. “Deep Spatial Autoencoders for Visuomotor Learning.” reconstruction 117.117 (2015): 240. 
  • Pinto, Lerrel, and Abhinav Gupta. “Supersizing Self-supervision: Learning to Grasp from 50K Tries and 700 Robot Hours.” arXiv preprint arXiv:1509.06825 (2015).

Deep Learning in Robotics

Traditional policy search approaches in reinforcement learning usually use the output of a “computer vision systems” and send commands to low-level controllers such as a PD controller. In the paper “end-to-end training of deep visuomotor policies”, Sergey, et al. try to learn a policy from low-level observations (image and joint angles) and output joint torques directly. The overall architecture is shown in the figure above. As you can tell this is ambitious and cannot be easily achieved without a few tricks. The authors first initialize the first layer with weights pre-trained on the ImageNet, then train vision layers with object pose information through pose regression. This pose information is obtained by having the robot holding the object with its hand covered by a cloth similar to the back ground (See figure below). robot collecting pose information

In addition to that, using the pose information of the object, a trajectory can be learned with an approach called guided policy search. This trajectory is then used to train the motor control layers that takes the visual layer output plus joint configuration as input and output joint torques. The results is better shown then described; see video below.

The second paper, “Deep Spatial Autoencoders for Visuomotor Learning”, is done by the same group in Berkeley. In this work, the authors try to learn a state space for reinforcement learning. Reinforcement learning requires a detailed representation of the state; in most work such state is however usually manually designed. This work automates this state space construction from camera image where the deep spatial autoencoder is used to acquire features that represent the position of objects. The architecture is shown in the figure below.

Deep Autoencoder in Robotics

The deep spatial autoencoder maps full-resolution RGB images to a down-sampled, grayscale version of the input image. All information in the image is forced to pass through a bottleneck of spatial features therefore forcing the network to learn important low dimension representations. The position is then extracted from the bottleneck layer and combined with joint information to form the state representation. The result is tested on several tasks shown in the figure below.

Experiments on Deep Auto Encoder

As I mentioned earlier gathering a large amount of training data in robotics is hard, while in the paper “Supersizing Self-supervision: Learning to Grasp from 50K Tries and 700 Robot Hours” the authors try to show that it is possible. Although still not comparable to datasets in the vision community such as ImageNet, gathering 50 thousand tries in robotics is significant if not unprecedented. The data is gathered using this two arm robot Baxter that is (relatively) mass produced compared to most research robots.

Baxter Grasping

 

The authors then use these collected data to train a CNN initialized with weights trained on ImageNet. The final output is one out of 18 different orientation of the gripper, assuming the robot always grab from the top. The architecture is shown in the figure below.

Grasping with Deep Learning

Distributed Code or Grandmother Cells: Insights From Convolutional Neural Networks

In Computer Vision, deep learning, Machine Learning, Neural Science, Sparse Coding on January 23, 2016 at 1:31 pm

by Li Yang Ku (Gooly)

grandmother-cell

Convolutional Neural Network (CNN)-based features will likely replace engineered representations such as SIFT and HOG, yet we know little on what it represents. In this post I will go through a few papers that dive deeper into CNN-based features and discuss whether CNN feature vectors tend to be more like grandmother cells, where most information resides in a small set of filter responses, or distributed code, where most filter responses carry information equally. The content of this post is mostly taken from the following three papers:

  1. Agrawal, Pulkit, Ross Girshick, and Jitendra Malik. “Analyzing the performance of multilayer neural networks for object recognition.” Computer Vision–ECCV 2014. Springer International Publishing, 2014. 329-344.
  2. Hinton, Geoffrey, Oriol Vinyals, and Jeff Dean. “Distilling the knowledge in a neural network.” arXiv preprint arXiv:1503.02531 (2015).
  3. Dosovitskiy, Alexey, and Thomas Brox. “Inverting convolutional networks with convolutional networks.” arXiv preprint arXiv:1506.02753 (2015).

So why do we want to take insights from convolutional neural networks (CNN)? Like what I talked about in my previous postIn 2012, University of Toronto’s CNN implementation won the ImageNet challenge by a large margin, 15.3% and 26.6% in classification and detection by the nearest competitor. Since then CNN approaches have been leaders in most computer vision benchmarks. Although CNN doesn’t work like the brain, the characteristic that makes it work well might be also true in the brain.

faceselectiv

The grandmother cell is a hypothetical neuron that represents a complex but specific concept or object proposed by cognitive scientist Jerry Letvin in 1969. Although it is mostly agreed that the original concept of grandmother cell which suggests that each person or object one recognizes is associated with a single cell is biological implausible (see here for more discussion), the less extreme idea of grandmother cell is now explained as sparse coding.

Deformable Part Model

Before diving into CNN features we look into existing computer vision algorithms and see which camp they belong to. Traditional object recognition algorithms either are part-based approaches that use mid-level patches or use a bag of local descriptors such as SIFT. One of the well know part-based approaches is the deformable part model which uses HOG to model parts and a score on respective location and deformation to model their spatial relationship. Each part is a mid-level patch that can be seen as a feature that fires to specific visual patterns and mid-level patch discovery can be viewed as the search for a set of grandmother cell templates.

SIFT

On the other hand, unlike mid-level patches, SIFT like features represent low level edges and corners. This bag of descriptors approach uses a distributed code; a single feature by itself is not discriminative, but a group of features taken together is.

There were many attempts to understand CNN more. One of the early work done by Zeiler and Fergus find locally optimal visual inputs for individual filters. However this does not characterize the distribution of images that cause a filter to activate. Agrawal et al. claimed that a grandmother cell can be seen as a filter with high precision and recall. Therefore for each conv-5 filter in the CNN trained on ImageNet they calculate the average precision for classifying images. They showed that grandmother cell like filters exist for only a few classes, such as bicycle, person, cars, and cats. The number of filters required to recognize objects of a class is also measured. For classes such as persons, cars, and cats few filters are required, but most classes require 30 to 40 filters.

convolutional-neural-networks-top-9-layer-4-5

In the work done by Hinton et al. a concept called distillation is introduced. Distillation transfers the knowledge of a cumbersome model to a small model. For a cumbersome model, the training objective is to maximize the probability of the correct answer. A side effect is that it also assigns probabilities to incorrect answers. Instead of training on the correct answer, distillation train on soft targets, which is the probabilities of all answers generated from the cumbersome model. They showed that the small model performs better when trained on these soft targets versus when trained on the correct answer. This result suggests that the relative probabilities of incorrect answers tell us a lot about how the cumbersome model tends to generalize.

Inverting CNN Features

On the other hand, Dosovitskiy et al. tried to understand CNN features through inverting the CNN. They claim that inverting CNN features allows us to see which information of the input image is preserved in the features. Applying inverse to a perturbed feature vector yields further insight into the structure of the feature space. Interestingly, when they discard features in the FC8 layer they found most information is contained in small probabilities of those classes instead of the top-5 activation. This result is consistent with the result of the distillation experiment mentioned previously.

Top-5 vs rest feature in FC8

These findings suggest that a combination of distributed code and some grandmother like cells may be closer to how CNN features work and might also be how our brain encodes visual inputs.

 

Deep Learning and Convolutional Neural Networks

In Computer Vision, deep learning, Machine Learning, Neural Science, Uncategorized on November 22, 2015 at 8:17 pm

by Li Yang Ku (Gooly)

Yann LeCun Geoff Hinton Yoshua Bengio Andrew Ng

Yann LeCun, Geoff Hinton, Yoshua Bengio, Andrew Ng

Well, right, nowadays it is just hard not to talk about Deep Learning and Convolutional Neural Networks (CNN) in the field of Computer Vision. Since 2012 when the neural network trained by two of Geoffrey Hinton’s students, Alex Krizhevsky and Ilya Sutskever, won the ImageNet Challenge by a large margin, neural networks have quickly become mainstream and made probably the greatest comeback ever in the history of AI.

alexnet

So what is Deep Learning and CNN? According to the 2014 RSS keynote speech by Andrew Ng , Deep Learning is more or less a brand name for all works related to this class of approaches that try to learn high-level abstractions in data by using multiple layers. One of my favorite pre-2012 work is the deep belief nets done by Geoffrey Hinton, Simon Osindero and Yee-Why Teh, where basically a multi-layer neural network is used to learn hand written digits. While I was still in UCLA, Geoffrey demonstrated this neural network during his visit in 2010. What is interesting is that this network not only classifies digits but can also be used to generate digits in a top down fashion. See a talk he did below for this work.


On the other hand, Convolutional Neural Networks (CNN) is a specific type of multi-layer model. One of the most famous work pre-2012 was on classifying images (hand written digits) introduced by Yann LeCun and his colleagues while he was at Bell Laboratories. This specific CNN, which is called the LeNet now, uses the same weights for the same filter across different locations in the first two layers, therefore largely reduces the number of parameters needed to be learned compared to a fully connected neural network. The underlying concept is fairly simple; if a filter that acts like an edge detector is useful in the left corner then it is probably also useful in the right corner.

imagenet

Both Deep Learning and CNNs are not new. Deep Learning concepts such as using multiple layers can be dated all the way back to 1975 when back propagation, an algorithm for learning the weights of a multi-layer neural network, was first introduced by Paul Werbos. CNNs on the other hand can also be traced back to around 1980s when neural network was popular. The LeNet was also work done around 1989. So why are Deep Learning and CNN suddenly gaining fame faster than any pop song singer in the field of Computer Vision? The short answer is because it works. Or more precisely, it works better than traditional approaches. A more interesting question would be why it works now but not before? The answer of this question can be narrowed down to three reasons. 1) Data: thanks to people posting cat images on the internet and the Amazon Mechanical Turk we have millions of labeled images for training neural networks such as the ImageNet. 2) Hardware: GPUs allow us to train multi-layer neural networks with millions of data within a few weeks through exploiting parallelism in neural networks. 3) Algorithms: new approaches such as dropout and better loss functions are developed to help train better networks.

ladygaga

One of the advantages of Deep Learning is that it bundles feature detection and classification. Traditional approaches, which I have talked about in my past post, usually consist of two parts, a feature detector such as the SIFT detector and a classifier such as the support vector machine. On the other hand, Deep Learning trains both of these together. This allows better features to be learned directly from the raw data based on the classification results through back propagation. Note that even though sparse coding approaches also learns features from raw images they are not trained end to end. It was also shown that through using dropout, an approach that simply randomly drops units to prevent co-adapting, such deep neural networks doesn’t seem to suffer an over fitting problem like other machine learning approaches. However, the biggest challenge lies in the fact that it works like a black box and there are no proven theories on why back propagation on deep neural networks doesn’t converge to a local minima yet. (or it might be converging to a local minima but we just don’t know.)

funny_brain_heart_fight

Many are excited about this recent trend in Deep Learning and associate it with how our own brain works. As exciting as I am, being a big fan of Neuroscience, we have to also keep in mind that such neural networks are proven to be able to approximate any continuous function based on the universal approximation theory. Therefore a black box as it is we should not be surprised that it has the capability to be a great classifier. Besides, an object recognition algorithm that works well doesn’t mean that it correlates to how brains work, not to mention that deep learning only works well with supervised data and therefore quite different from how humans learn. The current neural network model also acts quite differently from how our neurons work according to Jeff Hawkins, not to mention the fact that there are a large amount of motor neurons going top down in every layer in our brain that is not captured in these neural networks. Having said that, I am still embracing Deep Learning in my own research and will go through other aspects of it in the following posts.

 

 

One dollar classifier? NEIL, the never ending image learner

In Computer Vision, Machine Learning on November 27, 2013 at 5:18 pm

by Li Yang Ku (Gooly)

NEIL never ending image learner

I had the chance to chat with Abhinav Gupta, a research professor at CMU, in person when he visited UMass Amherst about a month ago. Abhinav presented NEIL, the never ending image learner in his talk at Amherst. To give a short intro, the following is from Abhinav

“NEIL (Never Ending Image Learner) is a computer program that runs 24 hours per day and 7 days per week to automatically extract visual knowledge from Internet data. It is an effort to build the world’s largest visual knowledge base with minimum human labeling effort – one that would be useful to many computer vision and AI efforts.” 

NEIL never ending image learner clusters

One of the characteristic that distinguishes NEIL from other object recognition algorithms that are trained and tested on large web image data set such as the ImageNet or LFW is that NEIL is trying to recognize images that are in a set that has unlimited data and unlimited category. At first glance this might look like a problem too hard to solve. But NEIL approaches this problem in a smart way. Instead of trying to label images one by one on the internet, NEIL start from labeling just the easy ones. Since given a keyword the number of images returned are so large using Google Image Search, NEIL simply picks the ones it feels most certain, which are the ones that share the most common HOG like features. This step also helps refining the query result. Say we searched for cars on Google Image, it is very likely that out of every 100 images there is one image that has nothing to do with cars (very likely some sexy photo of girls with file name girl_love_cars.jpg ). These outliers won’t share the same visual features as the other car clusters and will not be labeled. By doing so NEIL can gradually build  up a very large labeled data set from one word to another.

girl_love_car

NEIL also learns the relationships between images and is connected with NELL, never ending language learning. More details should be released in future papers. During the talk Abhinav said he plan to set up a system where you can submit the category you wanna train on and with just $1, NEIL will give you a set of HOG classifiers in that category in 1 day.

NEIL relationship

Viewing Computer Vision from a Bigger Picture

In Computer Vision, Machine Learning on April 5, 2012 at 10:38 pm

written by gooly (Li Yang Ku)

It’s easy to get lost when you are doing computer vision research, especially when you are deep in the codes tweaking parameters trying to improve while keeping balance. When you find yourself doing this for more than a half day, it’s probably a good time to lay back and look at the big picture.

For most computer vision problems, say object recognition, the quest is actually just trying to put data into different bins. Say we have a 200 by 200 grey image, we can just look at it as a point in a 200*200 = 40000 dimension space.  The problem now would be how to classify these points into different bins. In the paper “Origins of Scaling in Natural Images”, Ruderman shown that natural images have some common frequency spectrum. This suggests that natural images lies in a much smaller sub group in this immense dimension space. If we are able to map this high dimension point into a lower dimension while only throwing away uninformative data, we would be able to classify it easier.

Most of the vision work resides in this part, taking a high dimension data and turn it into a lower dimension data. SIFT points, HOG, SURF, and nameless researches are just doing this. Trying to find the lower dimension data that tells most.

And then we head to the second step where we have to classify these lower dimension data. It could be as simple as nearest neighbor, probability compared with your trained model or any machine learning algorithms such as Adaboost, SVM, neural network, etc. This step classifies all these points into different categories.

So back to where you were tweaking some magic parameters; what you are actually doing is probably slightly changing the sub space your images are mapped to, or throwing these points into bins slightly differently. So just take it easy, if it only works when you tweak it a lot, you are probably mapping to the wrong space or throwing points the wrong way.