We present an image analysis technique for obtaining the velocity distribution from image sequences taken with a Schlieren apparatus. With this technique, the image sequence is considered as a series of 2-D functions that are transforming gradually through the period when the image sequence is taken. The fluid movement between the two consecutive images is then obtained via functional analysis that gives the local function deformation at every image position. The velocity and acceleration of the flow field are derived. In contrast to the particle image velocimetry (PIV) techniques, the presented technique is advantageous in the situation where the tracing particles are difficult to introduce or identify. The Schlieren apparatus set up for the study is a modified positive-negative grid system. Buoyant flows produced from gas fires and gas explosion ejection are used as case studies.