Dynamic Pedobarography Transitional Objects by Lagrange’s Equation with FEM, Modal Matching and Optimization Techniques Raquel Ramos Pinho 1 , João Manuel R. S. Tavares 1, 2 1 FEUP – Faculdade de Engenharia da Universidade do Porto LOME – Laboratório de Óptica e Mecânica Experimental 2 DEMEGI – Departamento de Engenharia Mecânica e Gestão Industrial Rua Dr. Roberto Frias, s/n, 4200-465 PORTO, PORTUGAL {rpinho, tavares}@fe.up.pt Abstract. This paper presents a physics-based approach to obtain 2D or 3D dy- namic pedobarography transitional objects from two given images (2D or 3D). With the used methodology, we match nodes of the input objects by using mo- dal matching, improved with optimization techniques, and solve the Lagrangian dynamic equilibrium equation to obtain the intermediate shapes. The strain en- ergy involved can also be analysed and used to quantify local or global defor- mations. 1 Introduction Pedobarography is the measurement of dynamic variations in downward pressure by different areas of the foot sole, using a pedobarograph (apparatus for recording dy- namic variations as a person stands upright or walks). The recording of pedobarographic data during a normal walking step allows the dynamic analysis of the feet’s behaviour [1], [2]. For example diabetic patients suffer from irrigation problems which may cause ulcerations [2]. So, it is of interest to de- termine the conditions that can increase these occurrences, through the analyses of the temporal evolution of the support surfaces, the detection of the plantar hiperpressure zones, and the analysis of the spatial and temporal gradients of zones with higher pressure. The technical solutions used nowadays to analyse the sequences of pedobaro- graphic images have some deficiencies and are almost subjective [2]. On the other hand, it might be necessary to determine some intermediate pedobarographic images of a given sequence. So to estimate the transitional images we use a physics-based approach: we solve the Lagrange’s equation (LE) between the models built by the Fi- nite Element Method (FEM) [3], [4]. With this solution, as more nodes are matched, which can be improved by using modal matching with optimization techniques [5],