A Study of PHOC Spatial Region Configurations for Math Formula Retrieval

TL;DR

This paper investigates different PHOC spatial configurations, introducing concentric rectangles, to improve math formula retrieval, demonstrating that optimized PHOC levels outperform previous models and remain competitive with state-of-the-art methods.

Contribution

The study introduces concentric rectangle regions in PHOC, analyzes level redundancy, and shows improved retrieval performance over earlier PHOC configurations.

Findings

Rectangular PHOC levels outperform previous configurations.

Some PHOC levels are redundant and can be omitted.

PHOC models are competitive with state-of-the-art methods.

Abstract

A Pyramidal Histogram Of Characters (PHOC) represents the spatial location of symbols as binary vectors. The vectors are composed of levels that split a formula into equal-sized regions of one or more types (e.g., rectangles or ellipses). For each region type, this produces a pyramid of overlapping regions, where the first level contains the entire formula, and the final level the finest-grained regions. In this work, we introduce concentric rectangles for regions, and analyze whether subsequent PHOC levels encode redundant information by omitting levels from PHOC configurations. As a baseline, we include a bag of words PHOC containing only the first whole-formula level. Finally, using the ARQMath-3 formula retrieval benchmark, we demonstrate that some levels encoded in the original PHOC configurations are redundant, that PHOC models with rectangular regions outperform earlier PHOC models, and that despite their simplicity, PHOC models are surprisingly competitive with the state-of-the-art. PHOC is not math-specific, and might be used for chemical diagrams, charts, or other graphics.