Non-uniform Sampling for Unbiased Object Estimation

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Solution Overview

Problem

Current methods for estimating structural content in biological tissue, such as cancer cells in tissue slices, are time-consuming and require substantial work, with existing image analysis techniques being biased and unsuitable for biological cell counting.

Innovation Solution

A method involving non-uniform random sampling based on the likelihood of object presence in sectors, where sectors with higher probabilities of object presence are sampled more frequently, allowing for unbiased estimation of structural content using computer image analysis and the Horvitz-Thompson estimator.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If systematic uniform random sampling (SURS) is used to estimate structural content, then unbiased estimation is achieved, but substantial work and time are required

Engineering Contradiction:
Improveunbiased estimationVSAvoidprocessing time
Core Design Contradiction:
Measurement precisionVSLoss of time

Solution Approach 1:

The patent changes the sampling parameter from uniform probability to non-uniform probability proportional to the estimated structural content in each sector. This allows sectors with higher content to be sampled more frequently, improving estimation precision while reducing the total number of sectors that need to be examined, thus resolving the contradiction between unbiased estimation and processing time

Inventive Principle:
Principle #35Parameter changes

Solution Approach 2:

The patent performs preliminary image analysis on all sectors to estimate the structural content before the actual sampling process. This preliminary action creates a weighting scheme that guides the subsequent sampling, allowing the method to focus resources on sectors most likely to contain objects of interest, thereby reducing overall processing time while maintaining estimation accuracy

Inventive Principle:
Principle #10Preliminary action

2Extent of automation

If existing image analysis techniques are used for object counting, then automation is achieved, but the results are biased and unsuitable for biological cell counting

Engineering Contradiction:
ImproveautomationVSAvoidcounting accuracy
Core Design Contradiction:
Extent of automationVSMeasurement precision

Solution Approach 1:

The patent introduces an intermediary weighting factor based on estimated structural content that mediates between automated image analysis and final object counting. This intermediary layer corrects the bias inherent in standard image analysis by adjusting the sampling probability according to the likelihood of object presence, thereby maintaining automation while achieving accurate, unbiased counting results

Inventive Principle:
Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent modifies the sampling parameter from uniform random selection to non-uniform selection proportional to structural content estimates. This parameter change allows automated analysis to focus on high-probability sectors, reducing bias while maintaining the efficiency of automation

Inventive Principle:
Principle #35Parameter changes

Data Source

PatentEP2102817B1Method for unbiased estimation of the total amount of objects based on non uniform sampling with probability obtained by using image analysis
Publication Date: 2012.04.11 AARHUS UNIV
  • EP2102817B1 patent drawingFigure 1
  • EP2102817B1 patent drawingFigure 2
  • EP2102817B1 patent drawingFigure 3

AI summary

An image is partitioned into sectors, and a number of sectors are selected randomly but with a probability of selection which is proportional with the likelihood of objects in the sector. For the selected sectors, the objects are measured or counted and used for estimation of the amount of objects in the entire image.