<div>This thesis examines the multilinear equations of the calibrated pinhole camera. </div><div>The multilinear equations describe the linear relations between camera parameters and image observations in matrix or tensor formats. </div><div>This thesis includes derivations and analysis of the trilinear equations through the point feature relation. For the four-frame and more than four frame cases, this paper gives derivations and analysis using a combination of the bilinear and trilinear equations to represent general multi-frame point geometry. As a result, a three-frame model (TFM) for general multi-frame point geometry is given. This model provides a concise set of minimal and sufficient equations and minimal unknowns.</div><div> </div><div>Based on the TFM, there are two bundle adjustment (BA) approaches developed. </div><div>The TFM does not involve the object parameters/coordinates necessary and indispensable for the collinearity equation employed by BA. </div><div>The two methods use TFM as the condition equation fully and partially, replacing the collinearity equation. </div><div>One operation using both TFM and the collinearity equation is designed to engage the object structures' prior knowledge. </div><div>The synthetical and real data experiments demonstrate the rationality and validity of the TFM and the two TFM based methods. </div><div>When the unstable estimate of the object structures appears, the TFM-based BA methods have a higher acceptance ratio of the adjustment results. </div>