Resultados

A Figura 3.10 mostra a distor¸c˜ao espectral m´edia tanto para o Isomap quanto para o PCA. Note que a abordagem proposta usando o Isomap como t´ecnica de redu¸c˜ao de dimensionalidade fornece melhores resultados do que o PCA. Al´em disso, o Isomap gera menos distor¸c˜ao inclusive com menos dimens˜oes do que o PCA. Na Tabela 3.1 mostra-se o intervalo de confian¸ca (±2σ, 95%) para algumas dire¸c˜oes, onde observa-se que o Isomap apresenta menos variabilidade do que o PCA.

Por outro lado, como em outros estudos [69], a distor¸c˜ao espectral aumenta em altas frequˆencias devido `a complexidade do pavilh˜ao da orelha (veja a Figura 3.11). No entanto, na nossa abordagem a distor¸c˜ao fica, grosso modo, abaixo de 5 dB.

Tabela 3.1: Intervalo de confian¸ca (±2σ, 95%) da distor¸c˜ao espectral m´edia para v´arios azimutes.

Azimute Distor¸c˜ao Espectral M´edia (dB) Isomap

Distor¸c˜ao Espectral M´edia (dB) PCA -180 4.5 ± 1.1 6.7 ± 1.4 -100 4.7 ± 0.7 5.7 ± 3.2 0 5.0 ± 1.0 5.7 ± 3.0 100 4.9 ± 1.0 6.3 ± 3.7 145 4.7 ± 1.1 6.0 ± 2.3

Cap´ıtulo 3. Personaliza¸c˜ao de HRTFs usando Isomap no plano horizontal 38 x₁ x₂ x₃ x₄ d₁ d₂ d4 d₃ x1: Largura da cabeça x2: Profundidade da cabeça x3: Largura do pescoço x4: Largura dos ombros

d1: Largura do pavilhão da orelha d2: Altura do pavilhão da orelha d3: Largura da cavum concha d4: Altura da cavum concha

Cap´ıtulo 3. Personaliza¸c˜ao de HRTFs usando Isomap no plano horizontal 39 −150° −100° −50° 0° 50° 100° 150° 4. 5 5 5. 5 6 6 .5 7 7 .5 Azimute D ist o rçã o Esp e ct ra l Mé d ia (d B) ISOMAP PCA

Figura 3.10: Distor¸c˜ao espectral m´edia em fun¸c˜ao do azimute.

10 2 4 6 Frequência KHz D ist o rçã o Esp e ct ra l (d B) ISOMAP PCA 1 0.2 5

Cap´ıtulo

4

Conclus˜oes e Perspectivas

Conforme estudado nos dois primeiros cap´ıtulos, o problema do ´audio espacial envolve parˆametros tanto de engenharia quanto psicoac´usticos, sendo que os elementos principais da an´alise e s´ıntese do ´audio 3D s˜ao as HRTFs. Como as HRTFs variam amplamente entre indiv´ıduos, ´e necess´ario personaliz´a-las.

Com esse intuito, no Cap´ıtulo 3, propˆos-se um novo m´etodo para personalizar HRTFs no plano horizontal a partir de caracter´ısticas antropom´etricas. Al´em de usar o Isomap como m´etodo de redu¸c˜ao de dimensionalidade n˜ao linear, a principal contribui¸c˜ao deste trabalho ´e uma nova t´ecnica para construir o grafo do Isomap que incorpora informa¸c˜ao pr´evia importante sobre as HRTFs. Conforme mostrado nos resultados, o fato de incorporar conhecimento pr´evio na sele¸c˜ao dos vizinhos no Isomap pode levar a uma melhor representa¸c˜ao da variedade (i.e. manifold ) das HRTFs. Al´em disso, as simula¸c˜oes mostram que a abordagem proposta tem um desempenho melhor do que o PCA e confirmam que o Isomap ´e uma t´ecnica de redu¸c˜ao promissora para an´alise e s´ıntese de HRTFs, capaz de descobrir as rela¸c˜oes n˜ao lineares subjacentes da percep¸c˜ao auditiva.

Em pesquisas anteriores, com o intuito de ressaltar a individualidade das HRTFs ao longo das dire¸c˜oes e ouvidos, aplicaram-se m´etodos de redu¸c˜ao de dimensionalidade separadamente para cada dire¸c˜ao e ouvido. A desvantagem de aplicar m´etodos de redu¸c˜ao de dimensionalidade da forma mencionada, ´e que se perdem as rela¸c˜oes existentes ao longo das diferentes dire¸c˜oes e ouvidos. Assim, ´e importante ressaltar que na abordagem proposta nesta disserta¸c˜ao, para preservar essas rela¸c˜oes aplicou-se o m´etodo de redu¸c˜ao de dimensionalidade uma vez sobre todo o conjunto de dados de HRTFs para todos os indiv´ıduos, dire¸c˜oes e ouvidos no plano horizontal.

´

E importante tamb´em mencionar que, inicialmente, tentou-se usar o m´etodo de redu¸c˜ao de dimensionalidade LLE (Locally Linear Embedding) em vez do Isomap. Embora o LLE e o Isomap baseiem-se na constru¸c˜ao de um grafo para obter uma variedade, apenas a variedade obtida do Isomap conseguiu representar de forma adequada o conhecimento pr´evio que foi incorporado no grafo.

Cap´ıtulo 4. Conclus˜oes e Perspectivas 41

4.1

Perspectivas

O m´etodo de personaliza¸c˜ao de HRTFs proposto nesta disserta¸c˜ao precisa ser avaliado mediante experimentos psicoac´usticos. Estes experimentos dever˜ao analisar o desempenho da nossa abordagem na redu¸c˜ao de revers˜oes frente-tr´as e acima-abaixo assim como o erro de localiza¸c˜ao.

Outro aspecto relevante para futuras pesquisas ´e estender a abordagem proposta de persona- liza¸c˜ao de HRTFs al´em do plano horizontal. Conforme estudado no Cap´ıtulo 1, o ouvido humano ´

e capaz de estimar melhor a dire¸c˜ao de uma fonte no plano horizontal do que no plano mediano. Em geral, nossa precis˜ao na localiza¸c˜ao de fontes sonoras fora do plano horizontal diminui. Em virtude disso, um aspecto importante para futuros trabalhos ser´a procurar incorporar informa¸c˜oes relevantes da nossa percep¸c˜ao vertical na constru¸c˜ao do grafo do Isomap.

Como qualquer outra t´ecnica de redu¸c˜ao de dimensionalidade, o Isomap tem as suas desvan- tagens. Uma desvantagem do Isomap, ao contr´ario do PCA, ´e que ele gera um espa¸co de baixa dimensionalidade sem gerar uma fun¸c˜ao de mapeamento expl´ıcito. Assim, torna-se necess´ario usar algum tipo de aproxima¸c˜ao como a reconstru¸c˜ao baseada na vizinhan¸ca para reconstruir as amostras no espa¸co de alta dimensionalidade. Al´em disso, a falta de uma fun¸c˜ao de mapeamento expl´ıcito faz com que seja poss´ıvel projetar novas amostras (i.e. amostras fora da base de dados) no espa¸co de baixa dimensionalidade apenas atrav´es de aproxima¸c˜oes (e.g. a aproxima¸c˜ao de Nystrom [86]). No caso da abordagem proposta nesta disserta¸c˜ao, a aproxima¸c˜ao de Nystrom n˜ao foi capaz de projetar novas amostras de maneira adequada. Por conseguinte, um estudo futuro poderia realizar experimentos com t´ecnicas de redu¸c˜ao de dimensionalidade que forne¸cam uma fun¸c˜ao de mapeamento expl´ıcita.

Uma outra limita¸c˜ao da abordagem proposta ´e que a constru¸c˜ao do grafo do Isomap n˜ao leva em conta o conhecimento pr´evio das caracter´ısticas em frequˆencia das HRTFs. Esse fato, juntamente com a dificuldade de predizer as caracter´ısticas do pavilh˜ao da orelha, explica o incremento da distor¸c˜ao espectral em altas frequˆencias. Conforme estudado nos dois primeiros cap´ıtulos, sabe-se que os fatores que determinam a nossa percep¸c˜ao auditiva (e.g. IID, ITD, fatores espectrais) trabalham em diferentes faixas de frequˆencia. Portanto, fica para um trabalho futuro encontrar uma representa¸c˜ao que incorpore esse conhecimento pr´evio do comportamento espectral das HRTFs usando um banco de filtros.

Um dos inconvenientes na s´ıntese de ´audio espacial ´e que, devido `a dificuldade de medir as HRTFs, a quantidade dispon´ıvel de HRTFs medidas para indiv´ıduos diferentes ´e pouca. Al´em disso, a resolu¸c˜ao e as condi¸c˜oes de medi¸c˜ao variam ao longo das diferentes bases de dados de HRTFs. Por exemplo, a baixa resolu¸c˜ao espacial em dire¸c˜oes laterais da base de dados de HRTFs CIPIC afetou a constru¸c˜ao da variedade na abordagem proposta (i.e. os agrupamentos de HRTFs n˜ao est˜ao uniformemente distribu´ıdos na variedade da Figura 3.6b). Como trabalho futuro, seria interessante estudar a possibilidade de fazer a fus˜ao de v´arias bases de dados de HRTFs que foram medidas sob diferentes condi¸c˜oes e resolu¸c˜ao espacial.

Por outro lado, o m´etodo de regress˜ao usando redes neurais demonstrou ser capaz de predizer de forma correta as caracter´ısticas espectrais das HRTF a partir dos parˆametros antropom´etricos. Por´em, ainda ´e necess´ario diminuir a distor¸c˜ao espectral nas HRTFs preditas pela rede neural. Portanto, fica para um futuro estudo a an´alise de outras t´ecnicas de aprendizado de m´aquina.

Cap´ıtulo 4. Conclus˜oes e Perspectivas 42

Finalmente, fica para um trabalho futuro analisar a constru¸c˜ao da variedade das HRTFs de campo pr´oximo (i.e. HRTFs que dependem da dire¸c˜ao e da distˆancia) usando Isomap com o intuito de determinar se o Isomap ´e capaz de identificar os fatores de percep¸c˜ao de distˆancia. Nesse caso, o desafio seria introduzir o conhecimento pr´evio da nossa percep¸c˜ao de distˆancia na constru¸c˜ao do grafo do Isomap.

Publica¸c˜oes

Felipe Grijalva, Luiz Martini, Siome Goldenstein, and Dinei Florencio. Anthropometric based customization of Head-Related Transfer Functions using Isomap in the horizontal plane. In 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pages 4493-4497, Florence, Italy, May 2014.

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