Timur Khanipov

Timur M. Khanipov

It is demonstrated that the classical Hough transform with shift-elevation parametrization of digital straight lines has additive complexity of at most $\mathcal{O}(n^3 / \log n)$ on a $n\times n$ image. The proof is constructive and uses ensemble computation approach to build summation circuits. The proposed method has similarities with the fast Hough transform (FHT) and may be considered a form of the "divide and conquer" technique. It is based on the fact that lines with close slopes can be decomposed into common components, allowing generalization for other pattern families. When applied to FHT patterns, the algorithm yields exactly the $Θ(n^2\log n)$ FHT asymptotics which might suggest that the actual classical Hough transform circuits could smaller size than $Θ(n^3/ \log n)$.

Timur M. Khanipov

For the computational model where only additions are allowed, the $Ω(n^2\log n)$ lower bound on operations count with respect to image size $n\times n$ is obtained for two types of the discrete Radon transform implementations: the fast Hough transform and a generic strip pattern class which includes the classical Hough transform, implying the fast Hough transform algorithm asymptotic optimality. The proofs are based on a specific result from the boolean circuits complexity theory and are generalized for the case of boolean $\vee$ binary operation.

Evgeny Burnaev, Ivan Koptelov, German Novikov et al.

Recurrent Neural Networks (RNNs) are extensively used for time-series modeling and prediction. We propose an approach for automatic construction of a binary classifier based on Long Short-Term Memory RNNs (LSTM-RNNs) for detection of a vehicle passage through a checkpoint. As an input to the classifier we use multidimensional signals of various sensors that are installed on the checkpoint. Obtained results demonstrate that the previous approach to handcrafting a classifier, consisting of a set of deterministic rules, can be successfully replaced by an automatic RNN training on an appropriately labelled data.