In this article, we discuss the design of an optimal filter to detect objects that move linearly in dynamic images. With previous designs of filters to detect linear trajectory signals (LTS), the passband was set as the region of existence of LTS spectrum with some tolerance, while the rest was considered as the stopband. If two or more LTSs exist with different directions and velocities, however, their spectral domains are not necessarily exclusive (nonoverlapped). In this article, optimal filter theory is applied in a new way to the design of LTS detection filter. In so doing, spectra of signals to be extracted, or to be rejected, are treated as random variables, and the problem of minimization of error criteria is formalized as a stationary stochastic process. © 1999 Scripta Technica, Electron Comm Jpn Pt 1, 83(2): 42–51, 2000