I found some interesting papers using over-segmented data (voxel) concept and CRF with terrestrial LIDAR point cloud.
Volumetric Visualization of Multiple-return Lidar Data: Using Voxels by Jason Stoker [link]
Discriminative Learning of Markov Random Fields for Segmentation of 3D Scan Data by D. Anguelov, B. Taskar, V. Chatalbashev, D. Koller, D. Gupta, G. Heitz, and A. Ng. (CVPR2005)
Conditional Random Field for 3D point clouds with Adaptive Data Reduction by E. H. Lim and D. Suter (CW2007)
Multi-scale Conditional Random Fields for Over-segmented Irregular 3D Point Clouds Classification by E. H. Lim and D. Suter (CVPR2008)
3D terrestrial LIDAR classifications with super-voxels and multi-scale Conditional Random Fields by E. H. Lim and D. Suter (CVPR2008)
Shape-based Recognition of 3D Point Clouds in Urban Environments by Aleksey Golovinskiy et al (ICCV2009)
Recently, I have been working on Deformable-Structure Conditional Random Fields (DSCRFs) for image classification which is about CRFs that can change the graph structure to fit the data (image) and make inference (of pixel label) simultaneously. One problem of this approach is when we estimate the parameters (I guess everyone in the field knows what I’m talking about ^_^), so I’m looking for some optimization algorithms to deal with this. Of course, first thing I’m thinking of is variational approximation. I have tried some already such as mean-field, structure variational, but there is one popular method, “Contrastive Divergence” (CD), that I have heard and wanted to try. I have read some papers on it, and here are what I really recommend to read.
- “Note on Contrastive Divergence” by Oliver Woodford [pdf]: For me, this paper is the best; precise, intuitive and make you hungry to know more!
- “Training Products of Experts by Minimizing Contrastive Divergence” by Geoffrey E. Hinton [pdf]: I guess this is the original paper of CD. This is the first paper I read on this topic, the paper did a good job to make me understand the math underlying CD, however, I did not have an intuitive idea of what CD really is after that first reading. Surprisingly, after I read , then come back to , I found that I can put pieces together and get a better intuition of this topic. So, I really recommend reading  before .
Using Fast Weights to Improve Persistent Contrastive Divergence
In this article I compile a list of good papers and tutorials related to MRFs, CRFs and DRFs. Hopefully you will find it useful.
Recently I have been interested in conditional random fields (CRFs) for image modeling/labeling. I had really difficult time finding good materials to read. In this post, I would like to dedicate to people who are having a difficult time understanding CRFs, particularly, for image classification. My goal is to save your time by pointing you out to some good and useful materials, so that you don’t have to waste a lot of time like I did in past few weeks.
You might come up with some questions like what are the differences between CRF vs Bayesian networks (BNs) or between CRF vs MRF? What are the advantages of CRFs which are discriminative models over generative models like MRF and BN? What are the relationships between CRFs and other fundamental statistics models e.g. logistic regression and log-linear model? and most importantly…I’m a newbie..where should I get started?
Here are the list of materials:
- Log-linear Models and Conditional Random Fields by Charles Elkan http://videolectures.net/cikm08_elkan_llmacrf/ . I think this should be the first material you might want to learn from. The instructor did a really good job giving the overview of fundamental topics on statistics, e.g. maximum likelihood, logistic regression, log-linear model, then connect the idea to CRF at the end. However, in this lecture, there is not much connection between CRFs and other graphical models.
- Discriminative Random Fields (IJCV paper) by Sanjiv Kumar and Martial Hebert. For me, this is the best paper talking about CRFs for image classification/labeling. The paper discusses about MRF, BN in brief, then points out the main problems using those models, and shows how CRF can solve the existing problems.
- Models for Learning Spatial Interactions in Natural Images for Context-Based Classification (PhD thesis) by Sanjiv Kumar. If you like the paper  above and would like to see more detail of how to derive some learning formula, then you might want to see the PhD thesis of this paper which provides a lot mode details and images for better understanding.
- An Introduction to Conditional Random Fields for Relational Learning by Sutton, C., McCallum, A. (tutorial paper). This is a good and pretty long tutorial paper. What I like in this paper is that the paper motivates readers by some good examples especially in natural language processing which is a good application to show the power of CRFs. Another good thing is that this paper shows some connections between CRFs and some other graphical models.
At some point, you might feel that CRFs are closely related to MRFs. For those who are not familiar to MRFs, there are some good books and papers I would lkike to recommend:
- Markov random field modeling in image analysis by Stan Z. Li — This might be the best book on MRFs so far as it explains almost everything about MRFs in considerable details ranging from Gibbs random fields, MRFs, CRFs, DRFs, energy functions, smoothness constrains, learning algorithms, inference algorithms, etc. I really recommend this book if you have TIME to read it. However, this book seems to focus more on theoretical than real example aspect.
- Image processing: dealing with texture by Maria Petrou & Pedro García Sevilla — I like this book because there are a lot of good examples on how MRFs, energy functions, etc look like in practice. This would be a good book to read parallel to the book from Stan Z. Li.
- Image analysis, random fields, and dynamic Monte Carlo methods: a mathematical introduction by Gerhard Winkler
- Markov Random Field Models: A Bayesian Approach to Computer Vision Problems (technical report) by Gerda Kamberova. — This is a free, good , and concise report on MRFs or computer vision.