add k-d tree tutorial and update tree sub-module #771
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update tree sub-module with kd tree and tpr tree mixins
rcgorman-dstl
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hpritchett-dstl
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sdhiscocks
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jswright-dstl
| # .. image:: ../../_static/kd_tree_fig_2.png | ||
| # :width: 1200 | ||
| # :height: 250 | ||
| # :alt: Image showing diagrammatical representation of kd-tree in 2 dimensions, described further in figure 2 caption. |
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Figure 2B again.
Rather than saying move right because 8>5, it might be easier to follow if you show that you move right because abs(8-8) < abs(8-4) (Left descendant further from query node than right descendant in x dimension).
| # Searching a :math:`k`-d tree with Nearest Neighbour | ||
| # --------------------------------------------------- | ||
| # Once the :math:`k`-d tree has been constructed from the detection set, it can then be used to search for the Nearest | ||
| # Neighbour of a given track prediction (which is the query vector). |
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The query vector here would be the track prediction as seen in measurement space. I believe we refer to it as the measurement prediction.
…iption of traversing back up the kd tree during nearest neighbour search
…earch as requested in review
| # :alt: Image showing diagrammatical representation of kd-tree in 2 dimensions, described further in figure 2 caption. | ||
| # | ||
| # Fig. 2a offers a graphical representation of the :math:`k`-d tree shown in 2b. 2a shows the prediction vector, | ||
| # :math:`[8,2]`, in blue. 2b shows the first part of the search taking place down the :math:`k`-d tree. Current best |
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In the constructing a k-d tree section you state a vector space of [x, y]^T using :math:\begin{bmatrix} x \\ y \\\end{bmatrix}. However for the rest of the document each vector is displayed as math:[x, y]. It might be best for continuity/mathematical correctness to display each vector as math:[x, y]^T to denote that each is a vector in the same form as previously stated. You could use :math:\begin{bmatrix} x \\ y \\\end{bmatrix} throughout but it might make the lines break up a bit.
| # :math:`[8,2]`, in blue. 2b shows the first part of the search taking place down the :math:`k`-d tree. Current best | |
| # :math:`[8,2]^T`, in blue. 2b shows the first part of the search taking place down the :math:`k`-d tree. Current best |
| # | ||
| # All detections with :math:`x` coordinate :math:`\leq` the median are placed in the left subtree from the root node, | ||
| # and all detections with :math:`x` coordinate :math:`>` median are placed in the right subtree from the root node. The | ||
| # left and right subtrees are then split into two further subtrees in the same way, except this time using the values in |
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This explanation is so much better - really clear now
| # units, which becomes the new best distance. We then traverse back up the tree again. There are no other subtrees in | ||
| # the tree which can possibly contain detections that beat the current best distance, so the detection at :math:`[9,4]` | ||
| # is selected as the nearest neighbour and the search is complete when we reach the root. | ||
| # |
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One extra thought, what happens if both descendant nodes from the root node are an equal distance from the root node? Does the code account for this situation?
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update tree sub-module with kd tree and tpr tree mixins