B. Atal, J. Chang, M. Mathews, and J. Tukey, "Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer sorting technique," JASA 63, pp. 1535-1556, 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to other applications as well. However, how best to drive the face is a challenging question. A theoretical ideal driving source for face animation is speech acoustics, because the optical and acoustic signals are simultaneous products of speech production. Considerable research has been conducted [1, 2, 3] into the relationship between speech acoustics and the vocal tract shape. However, a direct examination of the relationship between speech acoustics and face movements has only recently been reported [4, 5] In [4] linear regression was used to examine relationships among tongue movements, ....

B. Atal, J. Chang, M. Mathews, and J. Tukey, "Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer sorting technique," JASA 63, pp. 1535-1556, 1978.

....one with the smallest length K T . Besides, SVD constructs an orthonormal base of the null space. So as a result, we have a complete specification of the solution set. In our case, as NU V (3 formants) QW YX (7 articulatory parameters) the null space dimension is 4. In the work of Atal [8], this space is a one dimensional space presented as a fiber. To retrieve all the solutions, we must determine this null space and then sample it: each sample gives rise to a solution. 3.3. Sampling the null space Let 324 be the particular solution given by the SVD method. The general form of ....

B. S. Atal, J. J. Chang, M. V. Mathews, and J. W. Tukey, "Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique," JASA, vol. 63, no. 5, pp. 1535--1555, May 1978.

....for each acoustic entry. As we did already explain, our hypercube codebook is a complete representation of the articulatory space, we did not eliminate any hypercube because that would constrain the inversion process. The only eliminated hypercubes are those which are situated in forbidden regions [1] because they do not correspond to any valid vocal tract shape (as explained in [6] The set of all the possible articulatory trajectories which may give rise to a given acoustic signal can be exploited to study the variability of the production of vowels and the compensatory effects used by a ....

B. S. Atal, J. J. Chang, M. V. Mathews, and J. W. Tukey. Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique. Journal of Acoustical Society of America, 63(5):1535-1555, May 1978.

....have used a more accurate test (but far more time consuming) which consists in evaluating the curvature along paths between any two vertexes of the hypercube. The greater the curvature is, the less linear the mapping is. When we decompose a hypercube, we may obtain a vertex in a forbidden region[6] i.e. a region with no acoustic parameters corresponding to articulatory ones, due to too strong a constriction in the vocal tract. These regions correspond to boundaries of the articulatory space the speaker can access when speaking. We therefore cannot define the hypercube vertexes in such ....

B. S. Atal, J. J. Chang, M. V. Mathews, J. W. Tukey, "Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique" Jour. Acoust. Soc. Am. vol. 63, N. 5, p1535-1555, 1978

....have used a more accurate test (but far more time consuming) which consists in evaluating the curvature along paths between any two vertexes of the hypercube. The greater the curvature is, the less linear the mapping is. When we decompose a hypercube, we may obtain a vertex in a forbidden region[6] i.e. a region with no acoustic parameters corresponding to articulatory ones, due to too strong a constriction in the vocal tract. These regions correspond to boundaries of the articulatory space the speaker can access when speaking. We therefore cannot define the hypercube vertexes in such ....

B. S. Atal, J. J. Chang, M. V. Mathews, J. W. Tukey, "Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique" Jour. Acoust. Soc. Am. vol. 63, N. 5, p1535-1555, 1978

.... the likelihood ratio[8] 1 n#S l #n#S r# 2 ###S l ####S r ## ###S l # # ##Sr ## (1) Many articulatory states may share the same acoustic distribution after the partition tree is constructed, with the underlying physical basis of manyto one mapping from articulation to acoustics[1]. which leads to one of the two hypotheses: # H0 : the observation set X#S# is generated from one distribution N #x; ##S#; ##; # H1 : the observation set X#S# is generated from two distributions N #x; ##S l #; ## and N #x; ##Sr #; ##. Use of the likelihood ratio in Eqn. 1) for deciding ....

....at least theoretically, by state clustering for use with a small amount of training data. the new decision tree algorithm we developed which is made specific to our articulatory feature based recognizer is grounded on the physical phenomenon of many to one articulation to acoustics relations [1]. Although overlapping of the output distributions associated with separate articulatory states already allows the recognizer to embody the many to one relations, this does not resolve the problem of training and testing mismatch exhibited by the presence of abundant unseen articulatory states ....

B. Atal, J. Chang, M. Mathews, and J. Tukey. "Inversion of articulatoryto -acoustic transformation in the vocal tract by a computer sorting technique, " JASA., Vol. 63, pp. 1535-1555,1978.

....is further enhanced in a optimization procedure. The algorithm we have adopted is based on a perturbation analysis of the differential contribution of each VT model parameter to each formant F 1 , F 2 and F 3 . This method was developed by [10] based on the theory of differential contribution [11]. The optimization procedure and the inferred improvements are described in detail in [12] One important issue here is the accepted error threshold of each formant DF n which may be selected from a combination of acoustic and perceptual criteria. We have chosen to define our convergence ....

Atal BS, Chang JJ, Mathews MV & Tukey JW (1978). Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique. J Acoust Soc Am, 63: 1535-1555.

....one with the smallest length jxj 2 . Besides, SVD constructs an orthonormal base of the null space. So as a result, we have a complete specification of the solution set. In our case, as M = 3 (3 formants) and N = 7 (7 articulatory parameters) the null space dimension is 4. In the work of Atal [8], this space is a one dimensional space presented as a fiber. To retrieve all the solutions, we must determine this null space and then sample it: each sample gives rise to a solution. 3.3. Sampling the null space Let Psvd be the particular solution given by the SVD method. The general form of ....

B. S. Atal, J. J. Chang, M. V. Mathews, and J. W. Tukey, "Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique," JASA, vol. 63, no. 5, pp. 1535--1555, May 1978.

....for each acoustic entry. As we did already explain, our hypercube codebook is a complete representation of the articulatory space, we did not eliminate any hypercube because that would constrain the inversion process. The only eliminated hypercubes are those which are situated in forbidden regions [1] because they do not correspond to any valid vocal tract shape (as explained in [6] The set of all the possible articulatory trajectories which may give rise to a given acoustic signal can be exploited to study the variability of the production of vowels and the compensatory e ects used by a ....

B. S. Atal, J. J. Chang, M. V. Mathews, and J. W. Tukey. Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique. Journal of Acoustical Society of America, 63(5):1535-1555, May 1978.

....distributions that give P(x c i ,j) We avoided limiting P(x c i ,j) because we want to allow for the various possible mappings from acoustics to articulator positions. For example, it has often been argued that many different articulator positions can be used to produce the same acoustic signal (Atal, Chang, Mathews Tukey, 1978; Schroeter Sondhi, 1994) Although the limited research on human speech production data argues that articulator positions can be recovered from acoustics much more accurately than computer simulations suggest (Hogden et al. 1996; Ladefoged, Harshman, Goldstein Rice, 1978; Papcun et al. ....

Atal, B. S., Chang, J. J., Mathews, M. V., & Tukey, J. W. (1978). Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique. Journal of the Acoustical Society of America, 63(5), 1535-1555.

....in the CM and j represents the PDF parameters (e.g. means and covariance matrices) These parameters constitute the MO MALCOM estimate of a probabilistic mapping between VQ codes and articulation. While it may or may not be possible to invert a deterministic mapping from articulation to acoustics (Atal, Chang, Mathews Tukey, 1978; Hogden et al. 1993) Bayes law makes it easy to invert MO MALCOM s probabilistic mapping to get the probability of a VQ code given a continuity map position, P c x , j [ p x c , j [ P c [ p x j [ EQ. 1 and analogous techniques are used to get the probability of each phoneme, ....

Atal, B. S., Chang, J. J., Mathews, M. V., & Tukey, J. W. (1978). Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique. Journal of the Acoustical Society of America, 63(5), 1535-1555.

....and articulatory parameters, then it is possible to represent acoustic constraints in the articulatory space, and combine them directly with minimum effort and continuity constraints. Such a combination is necessary once acoustic constraints do not uniquely determine the vocal tract geometry[18, 3, 4]. In [19] and [4] the vocal tract log area function was parametrized by a truncated Fourier cosine series. After that, the acoustic constraint imposed by the first three formant frequencies was combined with minimum effort constraints expressed by a quadratic cost function. Here, instead of a ....

B. S. Atal, J. J. Chang and J. W. Tukey: "Inversion of articulatory-to-acoustic transformation in the vocal-tract by a computing sorting technique", Journal of the Acoustical Society of America, 63, 5, pp. 1535--1555 (1978).

....be a more appropriate representation for recognition. Despite such attractions, articulatory parameters are not commonly used because of the difficulty in estimating them from speech. There is a complex mapping between the acoustic and articulatory domains, which is both non linear and non unique [1] [2] Such a relationship requires the use of non linear mapping techniques such as neural networks, non linear regression or the use of articulatory codebooks as reviewed in [2] In previous work we have attempted to overcome the difficulties mentioned by using articulatory codebooks with a ....

B. S. Atal, J. J. Chang, M. V. Mathews, and J. W. Tukey. Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique. J. Acoust. Soc. Am., 63:1535--1555, May 1978.

....considering the reasons why articulatory parameters are not commonly used for the analysis of speech. This is almost certainly due to the difficulty in estimating such parameters. There is a complex mapping between the acoustic and articulatory domains, which is both nonlinear and one to many [2] [3] Such a relationship requires the use of non linear mapping techniques such as neural networks, non linear regression or the use of articulatory codebooks as reviewed in [3] The principal aim of the work discussed in this paper is to develop a suitable method for the estimation of vocal ....

....problem were carried out by Mermelstein and Schroeder [9] 10] The method, based on perturbation theory, uses formant frequencies to estimate the vocal tract shape. The problems arising from the one to many mapping from the acoustic to articulatory domains were demonstrated by Atal et al. in 1978 [2]. Many area functions were determined that yielded the same acoustic parameters. Such area functions lie in a subset of articulatory space termed a fibre by the authors. This highlights a central difficulty in the inversion problem the uncertainty that results due to the one to many mapping. ....

B. S. Atal, J. J. Chang, M. V. Mathews, and J. W. Tukey. Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique. J. Acoust. Soc. Am., 63:1535--1555, May 1978.

....Thus, data driven reduction of the feature set (e.g. Principal Components Analysis (PCA) or Linear Discriminant Analysis (LDA) is usually required. Finally, the mapping from acoustics to articulation is not biunique: various articulatory constellations may produce highly similar acoustic signals [35, 3, 8]. 4 This entails the problem of reliably estimating articulatory features from the acoustic signal as well. On the other hand, high detection rates have been reported for articulatory features. Typically, frame accuracy rates range between 70 and 95 (e.g. 14, 7] with place features having ....

B.B. Atal, J.J. Chang, M.V. Mathews, and J.W. Tukey, "Inversion of articulatory-to-acoustic transformation in the vocal tract by a computersorting technique", Journal of the Acoustical Society of America 63, pp. 1535-1555, 1978

....speech synthesis, speech coding and teaching deaf people to speak. The solution of inverse mapping in speech is not trivial because the articulatory to acoustic transformation is nonlinear and of many to one type. A theoretical study of speech inversion has been done by Atal et al. 1978, [1], using a computer sorting technique. Other researchers have used nonlinear regression [10] Kalman filtering, 13] 9] artificial neural networks [7] inverse filtering [12] or VQ codebooks [5] In this paper we present our work toward improving the estimation of articulatory motion by Kalman ....

B. S. Atal, J. J. Chang, M. V. Mathews, and J. W. Tukey. Inversion of Articulatoryto -Acoustic Transformation in the Vocal Tract by a Computer-Sorting Technique. Journal of the Acoustical Society of America, 63(5):1535--1555, 1978.

....Honda studied the estimation of articulatory motion using an articulatory dynamical model and nonlinear filtering [11] They have used a nonlinear observation function relating the formant frequencies to articulatory parameters. A theoretical study of speech inversion has been done by Atal et al. [1], using a computer sorting technique. They studied the acoustic to articulatory relationship by sampling the whole space of an articulatory model and creating the articulatory sets of vectors called fibers which map into the same acoustic vector. A study of estimation of articulatory trajectories ....

B. S. Atal, J. J. Chang, M. V. Mathews, and J. W. Tukey. Inversion of Articulatory-to-Acoustic Transformation in the Vocal Tract by a Computer-Sorting Technique. JASA, 63(5):1535--1555, 1978.

....space has a unique image in the acoustic space, and every point in the acoustic space has an inverse image in the articulatory space (Schutz 1980, pp. 5 9) However, since the inverse image is not unique, the map is not a bijection (i.e. it is not a one to one mapping) Mermelstein 1967, Atal et al. 1978, Yehia and Itakura 1996) In principle, a map from the acoustic space to the articulatory space does not exist, since every map by definition must have a unique image (Schutz 1980, pp. 5 9) Nevertheless, it is possible to collapse the set of points that form the inverse image of a point in the ....

.... speaking, the procedures currently available can be divided into the following groups: model matching techniques (Mermelstein 1967, Ladefoged et al. 1978, Wakita 1979, Flanagan et al. 1979, Shirai and Kobayashi 1986, Yehia and Itakura 1996) codebook selection followed by fine optimization (Atal et al. 1978, Schroeter and Sondhi 1991) neural networks (Shirai 1993, Bailly et al. 1991) and even genetic algorithms (McGowan 1994) In any of these methods, it is necessary to cope with the fact that the dimensionality of the articulatory space is larger than that of the acoustic space. This can be done ....

B. S. Atal, J. J. Chang, and J. W. Tukey, 1978. Inversion of articulatory-to-acoustic transformation in the vocal-tract by a computing sorting technique. The Journal of the Acoustical Society of America, 63-5, 1535--1555.

....estimation from the speech signal. Following this line, various frameworks were formulated to combine the acoustic information contained in the speech signal with the constraints determined by the human physiology. A computer sorting technique followed by a fine optimization procedure was used by Atal et al. 1978) and, in a more elaborated model, by Schroeter and Sondhi (1991) Model matching techniques were used by Flanagan et al. 1980) and by Shirai and Kobayashi (1986) Shirai (1993) also proposed a neural network approach for the estimation of articulatory motion. Another connectionist approach, ....

....now on, the area function will be approximated by the first N = 9 terms of its log area Fourier cosine series expansion. 2. 2 Representing Morphological Constraints There are many sets of Fourier cosine coefficients that are associated with the same set of formant frequencies (Mermelstein, 1967; Atal et al. 1978). For this reason, it is necessary to impose constraints if we wish to estimate the area function from the formants. Figures 4 and 5 As an example, the thick solid lines shown in Figure 5 represent level curves of the surface shown in Figure 4; which shows the first formant frequency (F 1 in ....

[Article contains additional citation context not shown here]

B. S. Atal, J. J. Chang, and J. W. Tukey (1978), "Inversion of articulatory-to-acoustic transformation in the vocal-tract by a computing sorting technique", Journal of the Acoustical Society of America, Vol. 63, No. 5, pp. 1535--1555.

....and q(t) Another interpretation of these results can also suggest that consonants are characterized by various degrees of constraints on speci c articulators (Recasens, 1987) or regions of the vocal tract. 2.2. 2 The vocal tract variables The articulatory to audio visual transform is many to one: Atal, Chang, Mathews and Tukey (1978) de ne an articulatory i berj as the set of articulatory con gurations giving the same sound. Bo#, Perrier and Bailly (1992) show that these articulatory bers preserve the main geometric properties of the vocal tract, namely the constrictions. This motor equivalence is con rmed by bite blocks ....

....Matthies, Svirsky and Jordan, 1995; Guenther, 1995) This controller involves an acoustic to articulatory inversion. The problems arising from the non linearity of the articulatory to acoustic mapping and the excess of freedom of the inverse transform has been quite intensively presented (Atal et al. 1978; Sondhi and Gopinath, 1971; Sorokin, 1992; Jospa, Soquet and Saerens, 1992; Lin and Fant, 1989) 3 The Speech Maps computational model of control The schematic of the model we are using to invert from acoustical (distal) desired outcomes into articulatory (proximal) commands is shown in Fig. 1. ....

Atal, B. S., Chang, J. J., Mathews, M. V. and Tukey, J. W. (1978). Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer sorting technique, Journal of the Acoustical Society of America 63: 15351555.

....requirements are met [33, 107, 108, 172] An additional problem with the use of either virtual or physical targets is the fact CHAPTER 3. FROM PHONEMES TO ARTICULATORS 38 that quite different vocal tract shapes can be used to produce very similar acoustic output for some phonemes 11 [4, 94]. Thus multiple articulatory targets might exist for a given phoneme, with the vocal tract shape used for each individual instance being selected according to the context. A more realistic model would therefore require the use of context sensitive targets and or dynamics. As discussed in Section ....

.... of the central difficulties with any inverse mapping one which takes acoustic vectors at its inputs and predicts the values of the corresponding articulatory parameters at its outputs is the fact that quite different articulatory configurations can give rise to very similar acoustic outputs [4, 94]. This implies that attempts to model the inverse transformation using acoustic error alone [3, 61, 86, 122] are likely to produce discontinuous articulatory trajectories. A continuity constraint should therefore be applied to such trajectories, which may be implicit as in inverse filtering ....

B. S. Atal, J. J. Chang, M. V. Mathews, and J. W. Tukey. "Inversion of articulatoryto -acoustic transformation in the vocal tract by a computer-sorting technique". Journal of the Acoustical Society of America, 63(5):1535--1555, May 1978.

....vector, spectral vector) pairs [13] which is inverted using dynamic programming (DP) incorporating geometrical constraints on the articulator trajectories, as shown in figure 1. The inverse mapping is non unique, so dissimilar articulator positions may result in similar acoustic outputs [2, 7], hence attempts to model the inverse transformation using acoustic error alone [1, 10] are likely to produce discontinuous articulatory output. A continuity constraint should therefore be applied to such trajectories, which may be implicit as in inverse filtering techniques [16] or explicitly ....

B. S. Atal et al. "Inversion of articulatoryto -acoustic transformation in the vocal tract by a computer-sorting technique". J. Acoust. Soc. Am., 63(5):1535--1555, May 1978.

.... Barks might not require an intermediate formant description [13,27] However, most of the computational models for the effective formant F 0 2 are based on an intermediate formant detection (see [21] and characterisation, the control of acoustic stimuli in speech perception and inverse acoustics [1,4] is based on a formant representation of speech. Besides, new families of formant trackers [16,23] have shown that formants can be estimated accurately by imposing top down and continuity This work is supported by ESPRIT BR 6975 SpeechMaps. 2 constraints. This paper shows that formant ....

Atal, B.S., Chang, J.J., Mathews, M.V., and Tukey, J.W. Inversion of articulatory-toacoustic transformation in the vocal tract by a computer sorting technique. Journal of the Acoustical Society of America, 63:1535--1555, 1978.

.... (also see Markey, 1994; Menn Stoel Gammon, 1995; Perkell, Matthies, Svirsky, Jordan, 1995; Studdert Kennedy, 1993) Deriving this feedback is made difficult, however, by the fact that, whereas the mapping from articulation to acoustics is well defined, the reverse mapping is one to many (Atal, Chang, Mathews, Tukey, 1978). That is to say, essentially the same acoustics can be produced by many different articulatory configurations. For example, if no exhalation is allowed, then any static position of the tongue and jaw will result in silence. Silence maps to many possible articulatory states, but each of those ....

Atal, B. S., Chang, J. J., Mathews, M. V., & Tukey, J. W. (1978). Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer sorting technique. Journal of the Acoustical Society of America, 63, 1535--1555.

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B. S. Atal, J. J. Chang, M. V. Mathews, and J. W. Tukey, "Inversion of articulatory-to-acoustic transformation in the vocal tract by a computer-sorting technique," Journal of Acoustical Society of America, vol. 63, no. 5, pp. 1535--1555, May 1978.

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