New methods are developed for solving a class of inverse vision problems, where measured positions of stripe-shaped markers implanted in a deforming body of interest are used to find continuous descriptions of displacement and strain. Such methods have application in the area of magnetic resonance imaging of the heart, where it is now possible to implant and track transient stripes in the myocardium — a technique known as Spatial Modulation of Magnetization (SPAMM). Such methods make possible the measurement of strain in the heart. Curved-sided finite element models are used to fit displacement fields to observed marker positions based on a new type of constraint, called the straightness-spacing constraint, which makes maximum use of the information contained in SPAMM stripes. A new method of regularization, based on a rubber-like hyperelastic law, is introduced for ensuring smooth displacement fields which are insensitive to rigid body rotations and to the initial orientation of the undeformed body. These techniques are tested using 1) a gel annulus-shaped phantom; 2) a simulation model in which displacements are known analytically; and 3) SPAMM images from a human heart. Also presented is a method for checking the size of out-of-plane displacement terms which are normally neglected in the twodimensional calculation of strain.