Scale-space spatio-temporal random fields: Application to the detection of growing microbial patterns from surface roughness

• Spatio-temporal statistical modelling of surface roughness acquired at multiple time points.
• Scale-space analysis of multitemporal surface measurements.
• Statistical threshold based on scale-space spatio-temporal random field model.
• Detection of spatiotemporal patterns of unknown scales.
• Discrimination of spatiotemporal patterns based on the growth evolution.

Spatio-temporal statistical models have been receiving increasing attention in a variety of image processing applications, notably for detecting noisy patterns or shapes during their temporal evolutions. Space–time models are however still limited to detect accurately spatio-temporal patterns of multiresolution properties. To this end, the present paper addresses the detection of spatio-temporal patterns from multitemporal images at multiple scales. We propose a new stochastic model that incorporates scale-space and space-time models based on random fields—specifically, a scale space spatio-temporal Gaussian random field. Thereby, a statistical test to assess the null hypothesis (noise only) is computed by the expected Euler characteristic (EC) approach. A validation of our approach is investigated on synthetic examples using one dimensional signals. Then, a real application is carried out for detection of growing microorganisms from surface roughness, acquired at multiple time points. Based on the detection results, microbial colonies are thereafter discriminated through their scale and growth evolution. The results show the possibility of investigating robust and complete analysis in the context of precocious pattern detection.