The warp model of the extended Hough transform (EHT) has been proposed to design the explicit expression of the transform function of EHT. The warp model is a skewed parameter space (R(µ,ξ), φ(µ,ξ)) of the space (µ,ξ), which is homeomorphic to the original (ρ,θ) parameter space. We note that the introduction of the skewness of the parameter space defines the angular and positional sensitivity characteristics required in the detection of lines from the pattern space. With the intent of contributing some solutions to basic computer vision problems, we present theoretically a dynamic and centralfine/peripheral-coarse camera vision architecture by means of this warp model of Hough transform. We call this camera vision architecture askant vision' from an analogy to the human askant glance. In this paper, an outline of the EHT is briefly shown by giving three functional conditions to ensure the homeomorphic relation between (µ,ξ) and (ρ,θ) parameter spaces. After an interpretation of the warp model is presented, a procedure to provide the transform function and a central-coarse/peripheralfine Hough transform function are introduced. Then in order to realize a dynamic control mechanism, it is proposed that shifting of the origin of the pattern space leads to sinusoidal modification of the Hough parameter space.

Thus far, there have been many reports and publications on the algorithm for the efficient generation of a circle or an ellipse by the parametric method. In this parametric method, we compute a trigonometric function only at the time of setting the initial condition for generating graphics incrementally using the recurrence formula consisting of the arithmetical operations of addition, subtraction, and multiplication in the main loop. This means that the key to the faster generation of a circle or an ellipse is to reduce the number of multiplication operations. In the conventional methods, the numbers of multiplication operations required to generate a single point each for a circle and an ellipse are three and four, respectively. However, in this paper, we propose a method that makes it possible to generate a slanted ellipse by performing only two multiplication operations per point. The key to this is to use simultaneous recurrences. The proposed method allows a simpler initial setup than any of the conventional methods, thus performing the computation more efficiently. In addition, the new method proposed here causes no theoretical errors, with the rounding error being similar to or less than that of any conventional method.

FITH2 algorithm defined by the equations ρ=xcosθysinθ(π/(2K)). xsinθ at 0θπ/2 and ρ=xcosθysinθ(π/(2K))ycosθ at π/2θπ is a Hough transform which requires nothing of the trigonometric and functional operations to generate the Hough distributions. It is demonstrated in ths paper that the FIHT2 is a complete alternative of the usual Hough transform (HT) defined by ρ=xcosθysinθin the sense that the both tranforms could work perfectly as a line detector. It is easy to show that the Hough curves of the FIHT2 can be generated in an incremental way where only addition operations are needed. It is also investigated that the difference between HT and FIHT2 could be estimated to be neglected.