Rasterized Image Data Transformation Matrix Decomposition

Resolve Bottlenecks,
Find Innovative SolutionsGenerate Solutions

Solution Overview

Problem

Conventional systems face challenges in properly decomposing composite transformation matrices to align with the transformation order of rendering devices, leading to inefficiencies in rendering rasterized data, especially when rotation, scaling, and translation operations are performed in different orders.

Innovation Solution

A method and system that decompose composite transformation matrices into individual transformation operation matrices, using polar decomposition to derive rotation, scaling, and translation matrices, allowing for reordering to match the specific order of the rendering device's operations, enabling accurate transformation operations on rasterized data.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If conventional systems use composite transformation matrices for rendering, then transformation operations can be performed, but the systems cannot properly align with device-specific transformation orders

Engineering Contradiction:

Improveadaptability to device transformation ordersVSAvoidcomplexity of matrix decomposition and reordering

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent segments the composite transformation matrix into individual transformation operation matrices (rotation, scaling, translation) through polar decomposition. This segmentation allows each transformation component to be independently extracted and reordered to match device-specific requirements, resolving the contradiction between adaptability and complexity by breaking down the complex reordering task into manageable sequential steps.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent performs preliminary decomposition of the composite transformation matrix into individual transformation components before rendering. By pre-computing the polar decomposition and storing the individual transformation matrices, the system prepares the transformation data in advance, allowing flexible reordering without complex real-time calculations during rendering, thus reducing operational complexity while maintaining adaptability.

Inventive Principle:

Principle #10Preliminary action

2Manufacturing precision

If transformation matrices are decomposed into individual operations, then rendering accuracy improves, but processing time increases

Engineering Contradiction:

Improverendering accuracyVSAvoidprocessing time for matrix decomposition

Core Design Contradiction:

Manufacturing precisionVSLoss of time

Solution Approach 1:

The patent performs the computationally intensive polar decomposition and extraction of individual transformation parameters as a preliminary step before rendering. By completing the decomposition upfront and caching the individual transformation matrices, the system avoids repeated decomposition calculations, thereby maintaining high rendering accuracy while minimizing the time loss to a single decomposition operation rather than multiple iterative calculations.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent creates copies of the individual transformation operation matrices from the decomposed composite matrix. These copied individual matrices can be reused multiple times for different rendering operations without requiring re-decomposition, thus amortizing the initial processing time across multiple rendering tasks and improving overall efficiency while maintaining accuracy.

Inventive Principle:

Principle #26Copying

3Productivity

If algorithms are tightly coupled with hardware transformation orders, then processing efficiency is high, but adaptability to different devices is reduced

Engineering Contradiction:

Improverendering efficiencyVSAvoidcompatibility with different device orders

Core Design Contradiction:

ProductivityVSAdaptability or versatility

Solution Approach 1:

The patent segments the transformation process into independent operation matrices that can be individually reordered. This segmentation decouples the algorithm from hardware-specific transformation orders by allowing the same set of individual transformation matrices to be arranged in different sequences to match various device requirements, thus maintaining both efficiency and adaptability.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent introduces dynamic reordering capability where the sequence of transformation operations can be adjusted based on the target device's requirements. By making the transformation order flexible and device-adaptive rather than fixed, the system maintains high rendering efficiency for each specific device while achieving broad compatibility across different hardware configurations.

Inventive Principle:

Principle #15Dynamics

Data Source

PatentUS9626603B2Method and system for utilizing transformation matrices to process rasterized image data

Publication Date: 2017.04.18 XEROX CORP

AI summary

A method and system render rasterized data by receiving non-rasterized page description language data and a corresponding transformation matrix representing transformation operations to be performed. The non-rasterized page description language data is rasterizing to create rasterized data. The corresponding transformation matrix is decomposed into a plurality of individual transformation operation matrices and a discrete transformation operation value, from each corresponding individual transformation operation matrix, is generated for each transformation operation to be performed upon the rasterized data. The transformation operations are performed upon the rasterized data based upon the generated discrete transformation operation values.