The visual cortex is a well studied structure in the brain. Numerous laboratory tests have produced a wealth of data concerning the input-output behavior of the cortex. One of the main functions of the cortex is to detect lines in the visual image. Many theories as to how the cortex performs this task have been proposed. What we have done is to take several of these theories and combine them with the concept of a continuous-time, feedback system. Our results show that the orientation and length of the lines in an image can be detected using our system. This article is part one of two and covers the main detection engine consisting of Gabor filters used as the kernel of an integral transform.