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The 2 pictures above shown the 2 decision tree....
Question is: It is often claimed that a strength of decision trees is their interpretability.
Is this always justified? Refer to Figures 5 and 6 to help with your answer.
I think the point of the question is saying that a decision tree is interpretable if its depth is relatively small. The second tree is very deep i.e for one single prediction, you will get a high number of different splitting decisions to process. Therefore, you lose interpretability because the explanation for any prediction is an intersection of too many conditions for a human-user to process.
I have been studying DDA and Bresenham algorithms for line drawing and am curious about one thing.In both the algorithms,we consider a pixel grid to be of unit size and perform further steps.My question is if I change my grid size to say 0.5*0.5 instead of 1*1 grid,will there be any changes reflected in the way both algorithms work.If yes,can somebody enlighten me as to what those changes will be in each algorithm respectively.Very curious to know.Thanks for your answers in advance.Anybody who can help,please do so,since it urgent.I have an exam and I want this concept clarified.Please.Thanks:)
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I am trying to find the distance between two points on a triangulated surface (geodesic distance). It looks like a basic operation and is not trivial. So I am wondering if there are any libraries that do this? My google fo failed, so I would greatly appreciate any pointers.
(I am aware of CGAL, scipy.spatial, but I couldn't find anything in the docs, let me know if I missed something there)
There are many implementation for computing geodesic distance on triangle mesh. Some are approximate and some are exact.
1.Fast Marching method. This method is approximate and in practice the average error is below 1%. You can refer to Gabriel Peyre's implementation of fast marching method in matlab.
http://www.mathworks.com/matlabcentral/fileexchange/6110-toolbox-fast-marching
MMP method proposed by [1] and implemented in [2]. This method is exact and the code is in https://code.google.com/p/geodesic/ . Same as the comment by Ante. A disadvantage is that when the mesh is larege, MMP method will consume a lot of memory, O(n^2), n is the number of vertices.
CH method proposed in [3] and improved and implemented in [4]. This method is exact and consume less memory than MMP method. The code is in https://sites.google.com/site/xinshiqing/knowledge-share
Heat method proposed in [5]. One implementation is in https://github.com/dgpdec/course
This method is approximated and require a preprocessing process. It's faster than Fast Marching method.
[1] Joseph S. B. Mitchell, David M. Mount, and Christos H. Papadimitriou. 1987. The discrete geodesic problem. SIAM J. Comput. 16, 4 (August 1987), 647-668.
[2] Vitaly Surazhsky, Tatiana Surazhsky, Danil Kirsanov, Steven Gortler, Hugues Hoppe. Fast exact and approximate geodesics on meshes. ACM Trans. Graphics (SIGGRAPH), 24(3), 2005.
[3] Chen, J. and Han, Y.1990. Shortest paths on a polyhedron. InSCG '90: Proceedings of the sixth annual symposium on Computational geometry. ACM Press, New York, NY, USA, 360{369
[4] Shi-Qing Xin and Guo-Jin Wang. 2009. Improving Chen and Han's algorithm on the discrete geodesic problem. ACM Trans. Graph. 28, 4, Article 104 (September 2009), 8 pages.
[5] Crane K, Weischedel C, Wardetzky M. Geodesics in heat: a new approach to computing distance based on heat flow[J]. ACM Transactions on Graphics (TOG), 2013, 32(5): 152.
Just to add to the previous answer by wxnfifth that Fast marching method can be applied not alone, but as the first step to receive a good approximation of geodesic path, which is iteratively improved as follows:
Compose the strip of triangles containing existing approximation of the path.
Find the shortest path in the strip, which is a task that can be solved exactly in a linear time, for example by Shortest Paths in Polygons method by Wolfgang Mulzer.
If that path passes via a vertex on the boundary of triangle strip then the path along the other side of the vertex is considered, and if it is shorter then the strip is updated and the algorithm is restarted from step 2.
As to the libraries, where it is implemented, one can consider open-source MeshLib and specifically the function computeSurfacePath. And there is even a short video showing its work on some sample mesh.
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In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.
Their are many algorithms which exist for planar graph testing (i.e. determining if a given graph is Planar). The best ones are in O(n) where n is the number of vertices.
Which open source programs exist which support the following features:
Can Draw Planar Graphs
Support an O(n) Planar graph testing.
Support variable node size.
Support fixed drawing boundary region
Are open source
I have a few pointers for graph visualization methods:
Prefuse - original version is in Java and the newer stuff is flash.
Graphviz
Networkx with matplotlib - all in python
Ubigraph - for animated 3D visualization
I've found this one useful for all kinds of 2D work..
http://www.yworks.com/en/products_yed_about.html
It's java based so you should be able to run it anywhere you have a suitable jvm.
Graphanalyzer
From the site...
...
Graphanalyzer is an environment for visualization of graphs.
Graphanalyzer provides abilities for creating, processing of graphs
and shows the results of visualization. Program supports oriented and
nonoriented graphs, weighted and non weighted graphs. Program includes
many algorithms for graph processing, from path finding to planar
checking. This program is an irreplaceable helper for solving tasks
occurring in the graph theory. Visualization of graph and algorithm.
...
I'd suggest use build your own using boost-graph libraries. A good information can be found on Donald knuth home page. There are some softwares which I have not used very much. Graphthing is one of those. I do not think it'll meet your requirement. If you are a research guy, then I personally recommend not to be inclined towards visualization of graphs.
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Closed 10 years ago.
Does anyone know any good book or web resource for geometric and mathematical fundamentals of augmented reality?
Thanks!
Here's a good library for Augmented Reality:
ARToolKit
Ports to various platforms:
NyARToolKit
A simple but still impressive sample application using this library:
Project Marble
A great read is Chapter 10 of the Black Art of 3d Game Programming. All the AR/3D maths you'll ever need is there.
Once you've mastered this stuff, you'll be ready for 3d spatial projections etc, for AR/Target tracking.
I can't point any specific book right now, but depending on your math background I'd suggest go in this order
Vector and Linear algebra, intermediate level, up to matrix operation, LU decomposition, cross product.
Projective geometry, up to homogenious coordinates, planar homography
3d graphics, viewing and projection matrix, frustum
Basics of image processing, thresholds, edge detection, line detection
After those 4 two you can understand rectangular marker tracking
Calculus of many variables, Fourier transform, DFT
Least squares method
Intermediate linear algebra, eigenvalues, eigenvectors, SVD
Advanced numerical methods, nonlinear least-squares, Gauss-Newton, Levenberg-Marquardt
Advanced image processing, blob detection SIFT/SURF/FAST
Intermediate projective geometry: Essential and fundamental matrices, epipolar geometry
Bundle adjustment
After that you can understand markerless tracking
And some more advanced math which is used in cutting edge AR:
Understanding of basics of Lie groups and algebras
Statistics, robust estimators
Quaternions
Kalman filters
Clifford algebras (Geometric algebra) - generalization of quaternions
Wavelets
Advanced projective geometry (like trifocal tensor, 5-point algorithm)
I'd recommend the following two books. Both are pricey but contain lots of really useful stuff in Projective Geometry which is what you need to know.
It's hard going though so unless you really want to understand the maths behind it you may want to use a third party library as suggested above.
Multiple View Geometry in Computer Vision by Hartkey and Zisserman
and
Three Dimensional Computer Vision: A Geometric Viewpoint by Faugeras