Hierarchical multiple output gaussian processes for human motion data

Diferentes aplicaciones estadísticas implican el uso de diferentes parámetros y observaciones que en muchos casos están relacionadas de alguna manera dependiendo de la estructura del problema. Usualmente, estos parametros son usados como variables que codifican cierta información relacionada con las observaciones, además, ya estos parametros no son observables ni tampoco pueden ser medidos directamente, son inferidos de los datos observados gracias a las correlaciones dadas entre los mismos. De esa manera, se vuelve natural el modelar el fenómeno por medio de una estructura jerárquica en donde las variables observadas esten condicionadas a los parámetros, y a su vez estos parámetros condicionados a hiperparámetros, etc. Este tipo de modelos son relevantes en el sentido de que sirven cómo buenas aproximaciones al comportamiento de los datos. En el caso de regresión, modelos no paramétricos cómo los procesos Gausianos han sido propuestos también con algún tipo de estructura jerárquica, la cuál depende del problema a ser estudiado. Diferentes modelos jerárquicos han sido propuestos. Recientemente un novedoso método jerárquico para procesos Gausianos fue propuesto, en dicho modelo, se asumen que existen diferentes señales observadas que están relacionadas por una tendencia común a todas estas observaciones, la cuál puede ser predecida. Así, las señales observadas pueden ser vistas como versiones corruptas de esa tendencia común. Sin embargo, este tipo de modelos solo ha sido desarrollado para modelos de una sola salida, de esa manera se vuelve interesante explorar una extensión de este modelo a multiples salidas. Por tal motivo, en este trabajo se presenta una extension de un Proceso Gausiano jerÃarquico a multiples salidas, usando funciones de covarianza existentes con el objetivo de hacer interpolación y síntesis de movimiento humano. El modelo fue probado con datos tanto artificiales cómo reales, los resultados muestran que el modelo es exitoso interpolando y sintetizando movimiento humano en comparación a un modelo de procesos Gausianos de multiples salidas simple el cuál se usa en este trabajo como referencia

Hierarchical multiple output gaussian processes for human motion data

Diferentes aplicaciones estadísticas implican el uso de diferentes parámetros y observaciones que en muchos casos están relacionadas de alguna manera dependiendo de la estructura del problema. Usualmente, estos parametros son usados como variables que codifican cierta información relacionada con las observaciones, además, ya estos parametros no son observables ni tampoco pueden ser medidos directamente, son inferidos de los datos observados gracias a las correlaciones dadas entre los mismos. De esa manera, se vuelve natural el modelar el fenómeno por medio de una estructura jerárquica en donde las variables observadas esten condicionadas a los parámetros, y a su vez estos parámetros condicionados a hiperparámetros, etc. Este tipo de modelos son relevantes en el sentido de que sirven cómo buenas aproximaciones al comportamiento de los datos. En el caso de regresión, modelos no paramétricos cómo los procesos Gausianos han sido propuestos también con algún tipo de estructura jerárquica, la cuál depende del problema a ser estudiado. Diferentes modelos jerárquicos han sido propuestos. Recientemente un novedoso método jerárquico para procesos Gausianos fue propuesto, en dicho modelo, se asumen que existen diferentes señales observadas que están relacionadas por una tendencia común a todas estas observaciones, la cuál puede ser predecida. Así, las señales observadas pueden ser vistas como versiones corruptas de esa tendencia común. Sin embargo, este tipo de modelos solo ha sido desarrollado para modelos de una sola salida, de esa manera se vuelve interesante explorar una extensión de este modelo a multiples salidas. Por tal motivo, en este trabajo se presenta una extension de un Proceso Gausiano jerÃarquico a multiples salidas, usando funciones de covarianza existentes con el objetivo de hacer interpolación y síntesis de movimiento humano. El modelo fue probado con datos tanto artificiales cómo reales, los resultados muestran que el modelo es exitoso interpolando y sintetizando movimiento humano en comparación a un modelo de procesos Gausianos de multiples salidas simple el cuál se usa en este trabajo como referencia

Ensemble-characterisation of satellite rainfall uncertainty and its impacts on the hydrological modelling of a sparsely gauged basin in Western Africa

Many areas of the planet lack the infrastructure required to make accurate and timely estimations of rainfall. This problem is especially acute in sub-Saharan Africa, where a paucity of rain recording radar and sufficiently dense raingauge networks combine with highly variable rainfall, a reliance on agriculture that is predominantly rain fed and systems that are prone to flooding and drought. Satellite Rainfall Estimates (SRFE) are useful as they can provide additional spatial and temporal information to drive various downstream environmental models and early warning systems (EWS). However, when operating at higher spatial and temporal resolutions SRFE contain large uncertainties which propagate through the downstream models.This thesis uses the TAMSAT1 SRFE algorithm developed by Teo (2006) to estimate the rainfall over a large, data sparse and heterogenous catchment in the Senegal Basin. The uncertainty within the TAMSAT1 SRFE is represented using a set of ensemble estimates, each unique but equiprobable based on the full conditional distribution of the recorded rainfall, produced using the TAMSIM algorithm, also developed by Teo (2006). The ensemble rainfall estimates were then used in turn to drive a Pitman Rainfall-Runoff model of the catchment hydrology.The use of ensemble rainfall estimates was shown to be incompatible with the pre-calibrated parameter values for the hydrological model. A novel approach, the EnsAll method, was developed to calibrate the hydrological model which incorporated each individual ensemble member. The EnsAll calibrated model showed the greatest skill when driven by the ensemble rainfall estimates and little bias. A comparison of the hydrographs produced from TAMSIM ensemble rainfall estimates and that from an ensemble of perturbed TAMSAT1 estimates showed that the full spatio-temporally distributed method used by TAMSIM is superior to a simpler perturbation method for characterizing SRFE uncertainty.Overall, the SRFE used were shown to outperform the rainfall estimates produced from the sparse raingauge network as a hydrological model driver. However, they did demonstrate a lack of ability to represent the large interseasonal variations in rainfall resulting in large systematic biases. These biases were observed propagating directly to the modelled hydrological ouput

Ensemble-characterisation of satellite rainfall uncertainty and its impacts on the hydrological modelling of a sparsely gauged basin in Western Africa

Many areas of the planet lack the infrastructure required to make accurate and timely estimations of rainfall. This problem is especially acute in sub-Saharan Africa, where a paucity of rain recording radar and sufficiently dense raingauge networks combine with highly variable rainfall, a reliance on agriculture that is predominantly rain fed and systems that are prone to flooding and drought. Satellite Rainfall Estimates (SRFE) are useful as they can provide additional spatial and temporal information to drive various downstream environmental models and early warning systems (EWS). However, when operating at higher spatial and temporal resolutions SRFE contain large uncertainties which propagate through the downstream models. This thesis uses the TAMSAT1 SRFE algorithm developed by Teo (2006) to estimate the rainfall over a large, data sparse and heterogenous catchment in the Senegal Basin. The uncertainty within the TAMSAT1 SRFE is represented using a set of ensemble estimates, each unique but equiprobable based on the full conditional distribution of the recorded rainfall, produced using the TAMSIM algorithm, also developed by Teo (2006). The ensemble rainfall estimates were then used in turn to drive a Pitman Rainfall-Runoff model of the catchment hydrology. The use of ensemble rainfall estimates was shown to be incompatible with the pre-calibrated parameter values for the hydrological model. A novel approach, the EnsAll method, was developed to calibrate the hydrological model which incorporated each individual ensemble member. The EnsAll calibrated model showed the greatest skill when driven by the ensemble rainfall estimates and little bias. A comparison of the hydrographs produced from TAMSIM ensemble rainfall estimates and that from an ensemble of perturbed TAMSAT1 estimates showed that the full spatio-temporally distributed method used by TAMSIM is superior to a simpler perturbation method for characterizing SRFE uncertainty. Overall, the SRFE used were shown to outperform the rainfall estimates produced from the sparse raingauge network as a hydrological model driver. However, they did demonstrate a lack of ability to represent the large interseasonal variations in rainfall resulting in large systematic biases. These biases were observed propagating directly to the modelled hydrological ouput

Supplementing Frequency Domain Interpolation Methods for Character Animation

The animation of human characters entails difficulties exceeding those met simulating objects, machines or plants. A person's gait is a product of nature affected by mood and physical condition. Small deviations from natural movement are perceived with ease by an unforgiving audience. Motion capture technology is frequently employed to record human movement. Subsequent playback on a skeleton underlying the character being animated conveys many of the subtleties of the original motion. Played-back recordings are of limited value, however, when integration in a virtual environment requires movements beyond those in the motion library, creating a need for the synthesis of new motion from pre-recorded sequences. An existing approach involves interpolation between motions in the frequency domain, with a blending space defined by a triangle network whose vertices represent input motions. It is this branch of character animation which is supplemented by the methods presented in this thesis, with work undertaken in three distinct areas. The first is a streamlined approach to previous work. It provides benefits including an efficiency gain in certain contexts, and a very different perspective on triangle network construction in which they become adjustable and intuitive user-interface devices with an increased flexibility allowing a greater range of motions to be blended than was possible with previous networks. Interpolation-based synthesis can never exhibit the same motion variety as can animation methods based on the playback of rearranged frame sequences. Limitations such as this were addressed by the second phase of work, with the creation of hybrid networks. These novel structures use properties of frequency domain triangle blending networks to seamlessly integrate playback-based animation within them. The third area focussed on was distortion found in both frequency- and time-domain blending. A new technique, single-source harmonic switching, was devised which greatly reduces it, and adds to the benefits of blending in the frequency domain

Conditional Stochastic Simulation for Character Animation

Using motion capture data has nowadays utterly been adopted by video game creators or virtual reality applications. In a context of interactive applications, adapting those data to new situations or producing variants of those motions are known as non trivial tasks. We propose an original method that produces motions that preserve the statistical properties of a reference motion while ensuring some constraints. This method uses principles of conditional stochastic simulation to achieve this goal. Notably, a new real time algorithm, performing sequentially and producing the desired motion is introduced. Possible applications of our method are numerous and several examples are given, along with results

Conditional Stochastic Simulation for Character Animation

International audienceIn a context of interactive applications, adapting motion capture data to new situations or producing variants of them are known as non trivial tasks. We propose an original method that produces motions that preserve the statistical properties of a reference motion while ensuring some constraints. This method uses principles of conditional stochastic simulation to achieve this goal. Notably, a new real time algorithm, performing sequentially and producing the desired motion is introduced. Possible applications of our method are numerous and several examples are given, along with results