1,271 research outputs found
Segmentation and classification of individual tree crowns
By segmentation and classification of individual tree crowns in high spatial resolution aerial images, information about the forest can be automatically extracted. Segmentation is about finding the individual tree crowns and giving each of them a unique label. Classification, on the other hand, is about recognising the species of the tree. The information of each individual tree in the forest increases the knowledge about the forest which can be useful for managements, biodiversity assessment, etc. Different algorithms for segmenting individual tree crowns are presented and also compared to each other in order to find their strengths and weaknesses. All segmentation algorithms developed in this thesis focus on preserving the shape of the tree crown. Regions, representing the segmented tree crowns, grow according to certain rules from seed points. One method starts from many regions for each tree crown and searches for the region that fits the tree crown best. The other methods start from a set of seed points, representing the locations of the tree crowns, to create the regions. The segmentation result varies from 73 to 95 % correctly segmented visual tree crowns depending on the type of forest and the method. The former value is for a naturally generated mixed forest and the latter for a non-mixed forest. The classification method presented uses shape information of the segments and colour information of the corresponding tree crown in order to decide the species. The classification method classifies 77 % of the visual trees correctly in a naturally generated mixed forest, but on a forest stand level the classification is over 90 %
Exponential Time Complexity of the Permanent and the Tutte Polynomial
We show conditional lower bounds for well-studied #P-hard problems:
(a) The number of satisfying assignments of a 2-CNF formula with n variables
cannot be counted in time exp(o(n)), and the same is true for computing the
number of all independent sets in an n-vertex graph.
(b) The permanent of an n x n matrix with entries 0 and 1 cannot be computed
in time exp(o(n)).
(c) The Tutte polynomial of an n-vertex multigraph cannot be computed in time
exp(o(n)) at most evaluation points (x,y) in the case of multigraphs, and it
cannot be computed in time exp(o(n/polylog n)) in the case of simple graphs.
Our lower bounds are relative to (variants of) the Exponential Time
Hypothesis (ETH), which says that the satisfiability of n-variable 3-CNF
formulas cannot be decided in time exp(o(n)). We relax this hypothesis by
introducing its counting version #ETH, namely that the satisfying assignments
cannot be counted in time exp(o(n)). In order to use #ETH for our lower bounds,
we transfer the sparsification lemma for d-CNF formulas to the counting
setting
Let's Make Block Coordinate Descent Go Fast: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence
Block coordinate descent (BCD) methods are widely-used for large-scale
numerical optimization because of their cheap iteration costs, low memory
requirements, amenability to parallelization, and ability to exploit problem
structure. Three main algorithmic choices influence the performance of BCD
methods: the block partitioning strategy, the block selection rule, and the
block update rule. In this paper we explore all three of these building blocks
and propose variations for each that can lead to significantly faster BCD
methods. We (i) propose new greedy block-selection strategies that guarantee
more progress per iteration than the Gauss-Southwell rule; (ii) explore
practical issues like how to implement the new rules when using "variable"
blocks; (iii) explore the use of message-passing to compute matrix or Newton
updates efficiently on huge blocks for problems with a sparse dependency
between variables; and (iv) consider optimal active manifold identification,
which leads to bounds on the "active set complexity" of BCD methods and leads
to superlinear convergence for certain problems with sparse solutions (and in
some cases finite termination at an optimal solution). We support all of our
findings with numerical results for the classic machine learning problems of
least squares, logistic regression, multi-class logistic regression, label
propagation, and L1-regularization
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