Microsoft just recently presented the paper “High quality streamable free-viewpoint video
” at SIGGRAPH. In this presentation, they are capturing live 3D views of actors on a stage using multiple cameras and using computer vision to construct detailed texture mapped mesh models which are then compressed for live viewing. On the viewer you have the freedom to move around the model in 3D.
I contributed to this project for a year or so when I was employed at Microsoft, working on 3D reconstruction from multiple infra-red camera views, so it was nice to get an acknowledgment. Some of this work was inspired by our earlier work
at Microsoft Research which I co-presented at SIGGRAPH in 2004.
It’s very nice to see how far they have progressed with this project and to see the possible links that it can have with the Hololens
virtual reality system.
When training neural networks it is a good idea to have a training set which has examples that are randomly ordered. We want to ensure that any sequence of training set examples, long or short, has statistics that are representative of the whole. During training we will be adjusting weights, often by using stochastic gradient descent, and so we ideally would like the source statistics to remain stationary.
During on-line training, such as with a robot, or when people learn, adjacent training examples are highly correlated. Visual scenes have temporal coherence and people spend a long time at specific tasks, such as playing a card game, where their visual input, over perhaps hours, is not representative of the general statistics of natural scenes. During on-line training we would expect that a neural net weights would become artificially biased by having highly correlated consecutive training examples so that the network would not be as effective at tasks requiring balanced knowledge of the whole training set. Continue reading
If you are training neural networks or experimenting with natural image statistics, or even just making art, then you may want a database of natural images.
I generated an image patch database that contains 500,000 28×28 or 64×64 sized monochrome patches that were randomly sampled from 5000 representative natural images, including a mix of landscape, city, and indoor photos. I am offering them here for download from Dropbox. There are two files:image_patches_28x28_500k_nofaces.dat
The first file contains 28×28 pixel patches and the second one contains 64×64 patches. The patches were sampled from a corpus of personal photographs at many different locations and uniformly in log scale. A concerted effort was made to avoid images with faces, so that these could be used as a non-face class for face detector training. However there are occasional faces that have slipped through but the frequency is less than one in one thousand. Continue reading
Understanding the back-propagation algorithm for training neural networks can sometimes be challenging, because often there is a lot of confusing terminology which varies between sources. Also it is commonly described just in terms of the mathematics. Here I present a diagrammatic explanation of back-propagation for the visually inclined. I also summarize the non-linear stages that are commonly used, and provide some philosophical insight.
The forward pass though a neural net consists of alternating stages of linear multiplication by a weight matrix and non-linear activation functions which transform the output of each linear unit independently. We can write the transformation in vector form as
is the input,
is the output of the linear stage,
is the output of the non-linear stage, and
is the activation function which acts on each element of
independently. For subsequent stages, the input
is the output
of the previous stage. Continue reading
Having trained a two layer neural network to recognize handwritten digits with reasonable accuracy, as described in my previous blog post, I wanted to see what would happen if neurons were forced to pool the outputs of pairs of rectified units according to a fixed weight schedule.
I created a network which is almost a three layer network where the output of pairs of the first layer rectified units are combined additively before being passed to the second fully connected layer. This means that the first layer has a 28×28 input and a 50 unit output (hidden layer) with rectified linear units, and then pairs of these units are averaged to reduce the neuron count to 25, and then the second fully connected layer reduces this down to 10. Finally the softmax classifier is applied. Continue reading
In my last blog post I talked about trying out my code for training neural nets on a simple one-layer network which consists of a single weight layer and a softmax output. In this post I share results for training a fully connected two-layer network.
In this network, the input goes from 28×28 image pixels down to 50 hidden units. Then there is a rectified linear activation function. The second layer goes from the 50 hidden units down to 10 units, and finally there is the softmax output stage for classification.
When I train this network on the MNIST handwriting dataset I get a test error rate of 2.89% which is pretty good and actually lower than other results quoted on the MNIST web site
. It is interesting to inspect the patterns of the weights for the first layer below (here I organized the weights for the 50 hidden units as a 10×5 matrix): Continue reading
Recently I have been experimenting with a C++ deep learning library that I have written by testing it out on the MNIST handwritten digits data set. In this dataset there are 60,000 training images and 10,000 test images which are of size 28×28 pixels. I have been trying to reproduce some of the error rates that Yann LeCun reports on the MNIST site
. The digits written in many different styles and some of them are quite hard to classify, and so it makes a good test for neural net learning. Continue reading
When deriving sensory data from IMU chips it is always an issue that the gain and offset of the readings is not known, and varies from chip to chip. I have written a short Python script which uses a least squares fit to calibrate these devices. All you need to do is capture a set of XYZ readings while moving the device through different orientations, and put the readings in a text file. You can get this script from my github
I am passionate about machine learning, intelligence, and robotics. I have a number of robot projects on the go. I wanted to build a platform that would allow me to do a lot of complex experiments on sensor fusion and creating intelligent emergent behaviors. I needed to make a robot that has quite a number of sensor inputs, but not so many that it would overload the processing capability to do anything useful. I decided to make a simple two-wheeled robotic platform that has a lot of flexibility and load it up with appropriate sensors.
One of the aspects of my robotics philosophy is that information from simple sensors can be highly informative and that current robot designs jump too quickly to complex high bandwidth data sources and they then do a marginal job of interpreting the information from those sources in software. I am inspired by insects and other small creatures that seem to have small numbers of sensors, for example eyes with only a few photoreceptors, but still have very complex adaptive behaviors which are often leagues beyond what we can do with today’s machines. Part of this is due to the efficiency with which they extract every little bit of useful information out of the sensory data, including correlations we would never think of. I am interested in applying experience gained from machine learning in order to extract from sensors information that could not easily be determined by using hand coded algorithms.
My rolling robot has two wheels and these have wheel encoders to give a feedback of position or wheel rotation speed. It also has an infra red range finder that can indicate the Continue reading
I’m struggling with a health issue at the moment so I’m doing some some small projects to stay sane…
I’ve been helping a friend fix old pinball games which typically make use of 8-bit micros like the 6800 or 6502. Often we want to know what’s on these old ROM chips that even some modern device readers can’t easily scan. I built a shield for Arduino that can read them by listing the file over the serial link. The only components other than the Arduino Uno and a prototyping shield were a couple of 74HCT573s and a 24-pin socket. Continue reading