Ellipse Detection via Generalized Pascal Mapping

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Solution Overview

Problem

Existing ellipse detection methods consume excessive computing resources, making them inefficient in real-time applications, despite efforts to balance accuracy and efficiency.

Innovation Solution

An ellipse detection acceleration method based on generalized Pascal mapping is introduced, which selects valid candidate arc combinations using a small amount of computation, reducing invalid ellipse fitting and ensuring detection accuracy by employing edge detection, arc formation, and least squares methods to identify collinear points.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If Hough Transform or Probability Hough Transform is used for ellipse detection, then ellipse edges can be detected, but a large number of voting candidates consume excessive computing resources

Engineering Contradiction:

Improveellipse detection accuracyVSAvoidcomputation efficiency

Core Design Contradiction:

Measurement precisionVSProductivity

Solution Approach 1:

The patent segments the ellipse detection process into two stages: first using a simplified method to identify candidate arc combinations, then performing detailed ellipse fitting only on these candidates. This segmentation reduces the computational domain from all possible arc combinations to a small subset of promising candidates, resolving the contradiction between thorough detection and computational efficiency.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent performs preliminary action by pre-screening arc combinations using the generalized Pascal mapping property before actual ellipse fitting. By computing mapping points and checking collinearity in advance, it eliminates invalid candidates early, avoiding wasted computation on impossible ellipse configurations while maintaining detection accuracy.

Inventive Principle:

Principle #10Preliminary action

2Productivity

If geometric constraints of ellipse edges are used to reduce candidate objects, then computation is reduced, but it is difficult to balance accuracy and efficiency without relying on large computing resources

Engineering Contradiction:

Improvecomputation efficiencyVSAvoiddetection accuracy

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The patent changes the parameter representation by using generalized Pascal mapping to transform six arc parameters into three mapping point coordinates. This parameter transformation enables a simple collinearity check that is computationally efficient yet maintains the geometric constraints necessary for accurate ellipse detection, balancing both efficiency and precision.

Inventive Principle:

Principle #35Parameter changes

3Productivity

If arc-based ellipse detection methods are used to filter invalid combinations, then some acceleration is achieved, but ellipse parameters still need to be computed, so computation efficiency is not high enough

Engineering Contradiction:

Improvecomputation efficiencyVSAvoidoperating time

Core Design Contradiction:

ProductivityVSLoss of time

Solution Approach 1:

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent extracts the essential geometric constraint (collinearity of mapping points) from the complex ellipse fitting process. By separating this constraint check from the full ellipse parameter computation, it performs only the necessary minimum computation to validate candidates, significantly reducing operating time while preserving accuracy.

Inventive Principle:

Principle #2Taking out (Extraction)

4Measurement precision

If edge points are connected into arcs from real images, then accurate edge detection is achieved, but the large base number and discreteness of edge points require large computing resources

Engineering Contradiction:

Improveedge point accuracyVSAvoidcomputation resource requirement

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent segments the large set of discrete edge points into a smaller number of continuous arcs. By connecting adjacent edge points into arc segments, it reduces the data structure from thousands of individual points to a manageable number of arcs, simplifying subsequent processing while preserving edge accuracy.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent merges adjacent edge points into arc representations. By combining multiple discrete edge points into unified arc segments with defined endpoints and midpoints, it reduces computational complexity while maintaining the geometric information necessary for accurate ellipse detection.

Inventive Principle:

Principle #5Merging (Combining)

Data Source

PatentUS11783502B2Ellipse detection acceleration method based on generalized Pascal mapping

Publication Date: 2023.10.10 DALIAN UNIV OF TECH

AI summary

The present invention relates to the technical field of digital image processing, and provides an ellipse detection acceleration method based on generalized Pascal mapping. The method comprises: step 100, extracting accurate edge points from a real image by means an edge detection method of an ellipse detection method, connecting edge points into arcs, and taking a de-noised arc set as input of an ellipse detection acceleration method; step 200, screening out a valid candidate arc combinations probably belonging to the same ellipse from the arc set input in step 100; step 300, calculating five parameters of a candidate ellipse; repeating step 200 to step 300 until all valid candidate arc combinations in the arc set and corresponding candidate ellipses are found; and step 400, clustering and verifying candidate ellipse sets, obtaining a final detected ellipse set.