The Hough transform is a method for detecting shapes by applying a coordinate transformation to a picture such that all the points belonging to a curve of a given shape are transformed into a single location within the transformed space. The initial work concentrated how to detect analytic curves [16]. It was then generalized to detect nonanalytic curves [1, 12]. These methods were restricted to detecting a shape which is exact and, using pixels. This is called the Hough transform. We extend the capability of the Hough transform to detect an inexact shape (going a little away from the desired curve) by using the Hough transform and this will be called the inexact Hough transform. The input to the inexact Hough transform is lines instead of pixels. We first apply a line detection algorithm to find the lines in a picture and then used the lines as input to the inexact Hough transform. This approach not only makes the Hough transform faster, but also greatly improves its accuracy. The inexact Hough transform is applied to finding the rib cage from chest X-ray images, and shows good results.