The manipulation of soft materials has a wide range of applications in the industrial, service, and healthcare sectors. Possible applications range from plastering walls in the building construction industry to massaging patients and assisting in surgeries in medicine. Currently, robots lack the intelligence and perception capabilities to understand the properties of soft materials and estimate their spatial occupancy, which enables planning and control of physical interaction. Given a sequence of observations during the interaction of a robot manipulator with a soft material, an optimization problem can be defined to estimate the parameters of an underlying model which is determined a priori. The selected model should be computationally inexpensive and able to be used in a robot control framework. Additionally, the modeling method used should be able to represent the geometry of the object with sufficient accuracy so that it can be matched with real-world observations during model parameter estimation. This makes isogeometric analysis an ideal method to solve the modeling problem. In this contribution, as an initial approach to address the vision-based soft material parameter estimation problem, the axis-symmetric squeeze flow of a cylindrical soft material object is considered. An experimental setup has been designed consisting of two parallel plates where the upper plate is vertically displaced to compress the soft material while the lower plate remains stationary. An RGB camera is placed in front of the experiment setup to observe the change in the object's shape during compression. Isogeometric analysis is used to create a fast computational Stokes model, leveraging the properties of NURBs to still accurately represent geometry. The soft material parameter identification pipeline consists of three main modules: perception, modeling, and optimization. Once an RGB image is received from the camera, the perception pipeline extracts the borders of the soft material object observed from the camera using a combination of deep learning-based image segmentation and classical contour detection methods. The border observations obtained are then compared with the borders predicted by the IGA model. Ultimately, the model parameters minimizing the difference between the simulated and observed borders are obtained using a nonlinear least squares optimization scheme. The pipeline is then tested using photorealistic data from the squeeze-flow experiment