Maximum Inscribed Rectangle in Convex Polygon
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Solution Overview
Problem
Existing systems face difficulties in converting non-rectangular intersections of images into a rectangular shape with the same aspect ratio as the input images, particularly in combining images from high dynamic range or bracketed photography.
Innovation Solution
A computing device iteratively enlarges a rectangle within a convex polygon while maintaining a fixed aspect ratio, determining the maximum inscribed size by moving the rectangle based on the number of corners intersecting the polygon edges, until it can no longer be inscribed, allowing for efficient cropping and scaling.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing systems register and overlay individual images to produce a combined image, then the combined image can be produced from multiple input images, but the resulting combined image is non-rectangular in shape and difficult to convert to rectangular form
Solution Approach 1:
The patent extracts the essential rectangular region from the non-rectangular combined image by identifying the maximum inscribed rectangle within the convex polygon formed by the image boundaries. This extraction process isolates the usable rectangular content while discarding the irregular portions, solving the shape conversion problem.
Solution Approach 2:
The patent changes the parameter of the combined image from non-rectangular to rectangular by iteratively adjusting the rectangle's position and dimensions within the convex polygon. The algorithm modifies the rectangle parameters (x, y coordinates and width, height) until the maximum inscribed rectangle is found, achieving the desired rectangular shape.
2Manufacturing precision
If the combined image is converted to rectangular shape by existing systems, then the aspect ratio can be maintained, but the conversion process is difficult and complex
Solution Approach 1:
The patent employs a dynamic iterative approach where the rectangle is continuously adjusted in position and size within the convex polygon. The algorithm dynamically modifies the rectangle parameters through multiple iterations, moving the rectangle and changing its dimensions until the maximum inscribed rectangle is achieved, maintaining aspect ratio throughout the process.
Solution Approach 2:
The patent uses feedback by continuously checking whether the rectangle corners intersect with the convex polygon edges during the iterative process. This feedback mechanism guides the adjustment of rectangle position and size, ensuring the rectangle remains inscribed within the polygon while maximizing its dimensions and maintaining the aspect ratio.
3Area of stationary object
If a rectangle is inscribed within a convex polygon, then the largest possible rectangular region can be found, but an iterative process with multiple adjustments is required
Solution Approach 1:
The patent performs preliminary actions by first forming the convex polygon from the combined image boundaries and establishing the initial rectangle configuration before the iterative optimization begins. This preliminary setup includes determining the aspect ratio and initial position, which accelerates the subsequent iterative process by providing a good starting point.
Solution Approach 2:
The patent maintains continuity of useful action by iteratively enlarging the rectangle while moving it within the convex polygon without interrupting the optimization process. The algorithm continuously adjusts the rectangle parameters in a systematic manner, ensuring that each iteration builds upon the previous one to efficiently converge to the maximum inscribed rectangle.
Data Source
AI summary
Embodiments perform an iterative process for enlarging a rectangle having a fixed aspect ratio within a convex polygon to find the largest rectangular area within the convex polygon. The iterative process includes detecting an intersection of one or more corners of the rectangle with the convex polygon and adjusting a position of the rectangle based on the quantity of intersecting corners. The iterative growth process continues until a maximum inscribed size of the rectangle has been determined. Some embodiments process images from bracketed photography and crop areas outside the determined maximum inscribed size when combining the images into a single image.