Dense Graph Simplification via Salient Point Extraction
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Solution Overview
Problem
Existing graph simplification methods, such as the Douglas-Peucker algorithm, fail to effectively extract salient points from dense graphs, leading to incomplete representation of the original graph's features and difficulties in interactive control.
Innovation Solution
A method that extracts salient points by minimizing the greatest vertical distance between the original graph and lines connecting data points, using a salient point extracting unit with parallel GPU programming for accelerated calculations, and connects these points with a Catmull-Rom spline to adjust tangents, ensuring optimal simplification and user interaction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If the Douglas-Peucker algorithm is used for graph simplification, then the number of points is reduced, but the salient points are not properly extracted and the simplified graph does not accurately express features of the original graph
Solution Approach 1:
The patent changes the optimization parameter from simple point count reduction (Douglas-Peucker) to cost minimization where cost represents the greatest vertical distance between the original graph and simplified lines. This parameter change enables accurate feature representation while achieving simplification.
Solution Approach 2:
The patent replaces the greedy mechanical approach of Douglas-Peucker with a systematic optimization method using cost calculation and comparison. The system evaluates multiple candidate points and selects the optimal set that minimizes the maximum vertical distance, substituting heuristic mechanics with systematic optimization.
2Measurement precision
If more points are retained in the simplified graph, then feature accuracy is improved, but interactive control becomes difficult
Solution Approach 1:
The patent introduces a cost parameter (maximum vertical distance) as the optimization criterion, changing from simple point counting to distance-based optimization. This enables finding the optimal balance between point reduction and feature accuracy, making the simplified graph suitable for interactive control while preserving important features.
3Productivity
If the greedy method is used to incrementally add data points, then the process is simple and fast, but an optimized simplified graph cannot be extracted
Solution Approach 1:
The patent replaces the greedy incremental approach with a systematic cost-evaluation method. Instead of incrementally adding points based on simple criteria, the system calculates costs for candidate points and selects the optimal set that minimizes the maximum vertical distance, achieving better optimization quality.
Solution Approach 2:
The patent performs preliminary cost calculation for multiple candidate points before making the final selection. By pre-evaluating the cost (maximum vertical distance) for potential salient points, the system can make informed decisions to achieve optimal simplification rather than relying on incremental greedy choices.
Data Source
AI summary
Provided are a method, an apparatus and a system for dense graph simplification, and a recording medium for the same. The method includes receiving an original graph and extracting a plurality of salient points, which minimize a cost representing a greatest vertical distance between the original graph and each of a plurality of lines connecting two data points in a designated region on the original graph; and outputting a simplified graph in which the extracted salient points are connected. Thus, optimal results are ensured in dense graph simplification, and interactive control is allowed for a user.