Bézier Curve Shape Identification via Transformation Matrix
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Solution Overview
Problem
Conventional image recognition systems require significant computational resources and often fail to accurately identify shapes in images due to intensive processing, especially when dealing with larger or distorted objects, leading to increased computational costs and inaccuracies.
Innovation Solution
The use of Bézier curves to identify shapes in images by generating and comparing Bézier paths, which reduces computational costs and improves accuracy by accounting for size, rotation, and skew transformations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional pixel-based comparison methods are used for shape identification, then comprehensive shape analysis can be performed, but computational cost and processing time increase significantly
Solution Approach 1:
The patent segments the shape identification process into two distinct phases: (1) generating Bézier curve representations that capture essential shape characteristics, and (2) comparing these simplified representations. This segmentation reduces the computational burden by working with compact mathematical models rather than exhaustive pixel data, thereby decreasing processing time while preserving identification accuracy.
Solution Approach 2:
The patent extracts the essential geometric features of shapes by fitting Bézier curves to outline pixels. Instead of analyzing all pixels, the system extracts key control points and curve parameters that define the shape's geometry. This extraction process eliminates redundant information and focuses computation on the most discriminative features, reducing processing time without sacrificing accuracy.
2Measurement precision
If conventional pixel-based comparison methods are used for shape identification, then detailed shape characteristics can be analyzed, but computational resources are excessively consumed
Solution Approach 1:
The patent changes the representation parameters from raw pixel coordinates to Bézier curve control points and mathematical parameters. This parameter transformation compresses the data representation from potentially thousands of pixels to a small number of control points and curve coefficients, dramatically reducing memory usage and computational resources while maintaining the ability to accurately represent and compare shape geometries.
3Reliability
If conventional systems compare every edge pixel to identify shapes, then thorough shape verification can be achieved, but processing speed decreases
Solution Approach 1:
The patent performs preliminary action by generating Bézier curve representations before the comparison phase. The curve fitting process pre-processes the edge pixel data into a compact mathematical form that encodes the essential shape characteristics. This preliminary transformation enables rapid subsequent comparisons without sacrificing reliability, as the Bézier representations preserve the geometric fidelity needed for accurate shape identification.
4Measurement precision
If conventional systems perform intensive pixel comparisons, then accurate shape matching can be achieved, but the system cannot handle larger or distorted objects efficiently
Solution Approach 1:
The patent applies dynamics by making the shape representation adaptive through Bézier curves, which can dynamically adjust to represent shapes of varying sizes and degrees of distortion. The control points and curve parameters can be scaled and transformed to accommodate different object sizes and orientations, enabling the system to handle varied shapes efficiently while maintaining matching accuracy through the flexible mathematical representation.
Data Source
AI summary
The present disclosure is directed to identifying shapes in an image. For example, a shape identification system may identify an unknown shape represented by a Bézier path that has at least one Bézier curve. The shape identification system may also identify a stored Bézier path that has at least one stored Bézier curve, for example, in a database of known shapes. Using the Bézier curve of the unknown shape and the stored Bézier curve of the known shape, the shape identification system can determine a transformation matrix that transforms the transforms the Bézier curve of unknown shape to the stored Bézier curve of the known shape. Then, the shape identification system can compare the transformed Bézier curve to the stored Bézier curve to determine whether the unknown shape matches the known shape.