Vol. 29 No. 1 (2024): January-April


Computational Intelligence

Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning

Estimación de la aceleración a partir de una única imagen borrosa de movi-miento lineal uniforme utilizando el enfoque de mapeo homomórfico y apren-dizaje automático



acceleration, computer vision, deep learning, machine learning, motion blur, vision-based measurement (en).


aceleración, visión artificial, aprendizaje profundo, aprendizaje automático, desenfoque de movimiento, medición basada en la visión (es).

Abstract (en)

Context:  Vision-based measurement (VBM) systems are becoming popular as an affordable and suitable alternative for scientific and engineering applications. When cameras are used as instruments, motion blur usually emerges as a recurrent and undesirable image degradation, which in fact contains kinematic information that is usually dismissed.

Method: This paper introduces an alternative approach to measure relative acceleration from a real invariant uniformly accelerated linear motion-blurred image. This is done by using homomorphic mapping to extract the characteristic Point Spread Function (PSF) of the blurred image, as well as machine learning regression. A total of 125 uniformly accelerated motion-blurred pictures were taken in a light- and distance-controlled environment, at five different accelerations ranging between 0,64 and 2,4 m/s2. This study evaluated 19 variants such as tree ensembles, Gaussian processes (GPR), and linear, support vector machine (SVM), and tree regression.

Results: The best RMSE result corresponds to GPR (Matern 5/2), with 0,2547 m/s2 and a prediction speed of 530 observations per second (obs/s). Additionally, some novel deep learning methods were used to obtain the best RMSE value (0,4639 m/s2 for Inception ResNet v2, with a prediction speed of 11 obs/s.

Conclusions: The proposed method (homomorphic mapping and machine learning) is a valid alternative for calculating acceleration from invariant motion blur in real-time applications when additive noise is not dominant, even surpassing the deep learning techniques evaluated.

Abstract (es)

Contexto: Los sistemas de medición basados ​​en visión (VBM) están ganando popularidad como una alternativa asequible y apta para aplicaciones científicas y de ingeniería. Cuando se utilizan cámaras como instrumentos, el desenfoque de movimiento suele surgir como una degradación de imagen recurrente e indeseable, que de hecho contiene información cinemática que normalmente se descarta.

Método: Este artículo introduce un enfoque alternativo para medir la aceleración relativa a partir de una imagen borrosa real de movimiento lineal uniformemente acelerado invariante. Esto se hace utilizando mapeo homomórfico para extraer la point spread function (PSF) característica de la imagen borrosa, así como regresión de aprendizaje automático. Se tomaron un total de 125 imágenes borrosas de movimiento uniformemente acelerado en un entorno de luz y distancia controladas, en cinco aceleraciones diferentes en un rango de 0,64 a 2,4 m/s2. Este estudio evaluó 19 variantes tales como ensambles de árboles, procesos Gaussianos (GPR) y regresión lineal, regresión con máquina de vectores de soporte (SVM) y regresión con árboles.

Resultados: El mejor resultado de RMSE corresponde a GPR (Matern 5/2), con 0,2547 m/s2 y una velocidad de predicción de 530 observaciones por segundo (obs/s). Además, se utilizaron algunos métodos novedosos de aprendizaje profundo para obtener el mejor valor de RMSE (0,4639 m/s2 para Inception ResNet v2, con una velocidad de predicción de 11 obs/s.

Conclusiones: El método propuesto (mapeo homomórfico y aprendizaje automático) es una alternativa válida para calcular la aceleración a partir del desenfoque de movimiento invariante en aplicaciones en tiempo real cuando el ruido aditivo no es dominante, incluso superando las técnicas de aprendizaje profundo evaluadas.


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How to Cite


Cortés-Osorio, J. A., Gómez-Mendoza, J. B., and Riaño-Rojas, J. C. (2024). Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning. Ingeniería, 29(1), e20057.


Cortés-Osorio, J.A. et al. 2024. Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning. Ingeniería. 29, 1 (Mar. 2024), e20057. DOI:


Cortés-Osorio, J. A.; Gómez-Mendoza, J. B.; Riaño-Rojas, J. C. Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning. Ing. 2024, 29, e20057.


CORTÉS-OSORIO, Jimy Alexander; GÓMEZ-MENDOZA, Juan Bernardo; RIAÑO-ROJAS, Juan Carlos. Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning. Ingeniería, [S. l.], v. 29, n. 1, p. e20057, 2024. DOI: 10.14483/23448393.20057. Disponível em: Acesso em: 21 apr. 2024.


Cortés-Osorio, Jimy Alexander, Juan Bernardo Gómez-Mendoza, and Juan Carlos Riaño-Rojas. 2024. “Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning”. Ingeniería 29 (1):e20057.


Cortés-Osorio, J. A., Gómez-Mendoza, J. B. and Riaño-Rojas, J. C. (2024) “Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning”, Ingeniería, 29(1), p. e20057. doi: 10.14483/23448393.20057.


J. A. Cortés-Osorio, J. B. Gómez-Mendoza, and J. C. Riaño-Rojas, “Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning”, Ing., vol. 29, no. 1, p. e20057, Mar. 2024.


Cortés-Osorio, Jimy Alexander, et al. “Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning”. Ingeniería, vol. 29, no. 1, Mar. 2024, p. e20057, doi:10.14483/23448393.20057.


Cortés-Osorio, Jimy Alexander, Juan Bernardo Gómez-Mendoza, and Juan Carlos Riaño-Rojas. “Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning”. Ingeniería 29, no. 1 (March 14, 2024): e20057. Accessed April 21, 2024.


Cortés-Osorio JA, Gómez-Mendoza JB, Riaño-Rojas JC. Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning. Ing. [Internet]. 2024 Mar. 14 [cited 2024 Apr. 21];29(1):e20057. Available from:

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