2D Spatial Transformation via Surface Polynomial Grids
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Solution Overview
Problem
Existing image processing systems face limitations in representing general two-dimensional spatial transformations, particularly in hardware implementation, due to restrictions on complexity and data manipulation, leading to issues like data loss and inefficiency in applying geometric transformations.
Innovation Solution
A system and method for two-dimensional image transformation that uses a single-pass approach, involving a geometry input interface, grid transformation generator, patch geometry generator, surface function estimator, and output interface to parameterize the transformation as surface coefficients, allowing for efficient hardware implementation and flexible geometric mappings.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the two-pass method is used for image warping, then hardware implementation is simplified and real-time processing is enabled, but data loss occurs and geometric transformation flexibility is restricted
Solution Approach 1:
The patent divides the output image into multiple non-overlapping rectangular regions, each mapped to a corresponding region in the input image. This segmentation allows independent processing of each region while maintaining overall image integrity and avoiding the bottleneck effect that causes data loss in the two-pass method.
Solution Approach 2:
Instead of mapping input image regions to output image regions (forward mapping), the patent uses inverse mapping where each output pixel determines its corresponding input pixel coordinates. This inversion eliminates the data loss problem by ensuring every output pixel has a valid source, even when the intermediate image would be highly compressed.
2Manufacturing precision
If pixel-by-pixel description (lookup tables) is used to enhance the two-pass method, then transformation accuracy is improved, but storage space requirements increase and additional data manipulation becomes complex
Solution Approach 1:
The patent represents each regional transformation using a small number of parameters (polynomial coefficients) rather than storing complete pixel-by-pixel lookup tables. This parameterization maintains transformation accuracy while dramatically reducing storage requirements and enabling simple operations like zooming by modifying parameters rather than regenerating entire data structures.
Solution Approach 2:
The patent uses adjustable polynomial parameters to represent transformations, allowing dynamic modification of transformation characteristics (such as zoom level) by changing parameters rather than restructuring data. This provides flexibility for additional data manipulations without regenerating the entire transformation grid.
3Productivity
If restricted subset of 2D transformations is used in single-pass systems, then hardware implementation efficiency is improved, but general 2D mapping capability is lost
Solution Approach 1:
The patent segments the image into multiple regions, each with its own polynomial transformation parameters. This allows complex general 2D mappings to be represented as compositions of simpler regional transformations, maintaining hardware efficiency while achieving versatility.
Solution Approach 2:
The patent creates a unified framework where a single polynomial-based representation can describe various transformation types (affine, perspective, and more complex mappings). By using adjustable polynomial orders and regional decomposition, the system achieves universal applicability for general 2D mappings while maintaining hardware implementation efficiency.
Data Source
AI summary
A system and method for representing a two-dimensional spatial transformation that describes the transformation by an inverse mapped grid data set. The grid data for each coordinate is surface fitted on an array of rectangular patches defined in the output space using numerical techniques. Error analysis determines whether a finer mesh resolution is required for surface fitting. The spatial transformation is then defined by the array of rectangular surface patches and the set of surface coefficients such that the spatial transformation can be executed through evaluation of the surface polynomials. The two-dimensional surface polynomial representation allows the transformation to be easily adjusted for scale changes and zooming and panning effects.