Abstract: A method of installing piping of a floor heating apparatus according to the present invention relates to a method of installing a floor heating apparatus in which pipes for circulating heat medium liquid are located on a floor base structure and they are covered with a flowable floor substrate material. After an adhesive is applied on a surface of the floor base structure, a tube assembly is positioned on said adhesive so that the lower face of a base plate of the tube assembly is bonded to said floor base structure by means of said adhesive, the tube assembly having a plurality of tubes made of an elastic material and said base plate made of the elastic material which integrally carries said tubes. A self-leveling material is poured and extended on the tube assembly. According to such a construction method, a number of floor heating pipes can be quickly and simply installed on a floor surface and a density of installation of floor heating pipes can be relatively readily increased.

Abstract: Each of a certain number of sequences of binary pixels chosen according to some prescribed rules from m.times.n matrix of pixcels is referred to vector v.sub.i. A standard character k is represented with m.times.n matrix of binary pixels, from which the vectors g.sub.ki are derived. The reference vectors G.sub.ki are comprised of the vectors g.sub.ki and g.sub.ki which are generated by modification of g.sub.ki. A recognition object is captured to yield m.times.n matrix of binary pixels, from which the vectors v.sub.i are derived for comparison with the reference vectors G.sub.ki. Matching of v.sub.i with one of the reference vectors G.sub.ki adds a count to the standard pattern k corresponding to G.sub.ki. The standard character k with the maximum score of the matching count is recognized as the recognition object.