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Probability Histograms01:17

Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
Probability Distributions01:32

Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Probability Laws01:49

Probability Laws

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Related Experiment Video

Updated: Jun 23, 2026

Three-Dimensional Shape Modeling and Analysis of Brain Structures
05:33

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

3D model retrieval using probability density-based shape descriptors.

Ceyhun Burak Akgül1, Bülent Sankur, Yücel Yemez

  • 1Video Processing and Analysis Group, Philips Research Europe, High Tech Campus 36 (WOp122 O-1), 5656AE Eindhoven, The Netherlands. ceyhun.akgul@philips.com

IEEE Transactions on Pattern Analysis and Machine Intelligence
|April 18, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a novel 3D object retrieval method using probabilistic generative descriptions of local shape properties. The density-based descriptor ensures accurate and robust 3D model identification across diverse datasets.

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Area of Science:

  • Computer Vision
  • 3D Shape Analysis
  • Geometric Modeling

Background:

  • Content-based 3D object retrieval is crucial for managing large 3D model databases.
  • Existing methods often struggle with shape variations and mesh resolution.
  • A robust and efficient shape descriptor is needed for accurate retrieval.

Purpose of the Study:

  • To develop a probabilistic generative framework for describing local shape properties of 3D objects.
  • To enable efficient and invariant content-based retrieval of complete 3D object models.
  • To achieve state-of-the-art discrimination for diverse 3D shape categories.

Main Methods:

  • Characterizing 3D objects using multivariate probability density functions of local surface features.
  • Employing kernel density estimation (KDE) and fast Gauss transform for descriptor computation.
  • Utilizing density-based characterization for permutation invariance in shape matching.

Main Results:

  • The proposed density-based descriptor is efficiently computed and robust to shape perturbations and mesh resolution.
  • The framework guarantees invariance at the shape matching stage due to its permutation property.
  • Extensive experiments demonstrate state-of-the-art discrimination capabilities on heterogeneous 3D databases.

Conclusions:

  • The probabilistic generative description framework offers a powerful approach for 3D object retrieval.
  • The method provides robust, efficient, and invariant shape characterization.
  • This work advances the field of content-based 3D model retrieval with superior performance.