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Generování hudebních symbolů pomocí neuronových sítí
Havelka, Jonáš ; Pecina, Pavel (advisor) ; Hajič, Jan (referee)
We create more training data for the optical music recognition (OMR) task by generating artificial images of the music symbols. We follow up Mashcima and the model J. Mayer trained on it. We take the Rebelo dataset (dataset of music symbol images), adjust it with some computer vision methods, and train generative neural networks (above all, variational and adversarial autoencoders) on it. By replacing some original images in Mashcima input with ones generated by those networks, we get more general performance from the model: For slightly worsening on the original dataset (CVC-MUSCIMA), we get much better results on the PrIMuS dataset. Also, we create very realistic synthetic images of music symbols.
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Banach-Mazur distance between Banach spaces of continuous functions
Havelka, Jonáš ; Cúth, Marek (advisor) ; Rondoš, Jakub (referee)
In this bachelor thesis, we examine estimates of a Banach-Mazur distance between spaces C(ω) and C(ω · k) for various k ∈ N. With a properly chosen form of mapping, we constructively show the best currently known upper bounds of this distance for all k. Besides the known bounds d(C(ω), C(ω · k)) ≤ 2 + √ 5 for any k > 3, and d(C(ω), C(ω · 2)) ≤ 3, we are going to find, for k = 3, the better bound, namely d(C(ω), C(ω · 3)) ≤ 4 instead of already known 2 + √ 5. 1
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