Classical versus Deep Mirror-Symmetry Scoring: A Benchmark of Thirteen Methods

Jul 16, 2026

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Mirror-symmetry scoring quantifies how closely an image matches reflection symmetry about a specified axis, supporting uses ranging from visual aesthetics to medical and developmental analysis. Prior symmetry scorers lacked a shared, statistically grounded evaluation protocol. This work benchmarks thirteen scoring methods—nine from literature and four newly introduced—across four single-axis and five multi-axis datasets under a reflection-exact protocol. Frozen deep-feature approaches lead, while a tuned HOG baseline is only slightly behind, with discrimination concentrating in mid-scale oriented features.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages22

Reading Time55 min

Introduction

Problem distinction: detection vs scoring

Related Work

Symmetry Detection

Article Classical versus Deep Mirror-Symmetry Scoring: A Benchmark of Thirteen Methods Maximilian Woehrer 1, * arXiv :2607 .08379v 1 [ cs .CV] 9 Jul 2026 1 Research Group Software Architecture, Faculty of Computer Science, University of Vienna, Vienna, Austria; [maximilian.woehrer@univie.ac.at](maximilian.woehrer@univie.ac.at) Abstract Quantifying how mirror-symmetric an image is about a given axis (symmetry scoring) underpins applications from visual aesthetics to medical imaging, yet proposed scoring methods have never been compared on a common, statistically grounded protocol. We benchmark 13 scoring methods (nine collected from literature, four introduced here) spanning from classical features to frozen deep features, across four single-axis and ﬁve multiaxis datasets under a reﬂection-exact protocol with a chance-anchored, signiﬁcance-tested discrimination skill. Deep backbones perform best on single-axis and harder multi-axis protocols. However, a classical histogram-of-oriented-gradients (HOG) descriptor trails the best frozen-network readout by a small (but signiﬁcant) margin, is not statistically separable from the runner-up (a CNN-ﬁlter measure), and runs ∼300 × faster on CPU. Our results show that discrimination concentrates in mid-scale oriented features, where deep backbones peak at a low or mid stage, and HOG peaks at a mid cell size. Among existing methods, frozen deep features thus offer little over a tuned classical descriptor for measuring symmetry; whether task-trained deep scorers can do better remains open. We release the scorers and harness in imgsym, an open toolkit for image symmetry detection and measurement. Keywords: symmetry scoring; mirror symmetry; reﬂection symmetry; symmetry axis discrimination; histogram of oriented gradients; deep features; benchmark 1. Introduction Bilateral (mirror) symmetry is one of the most striking patterns in natural and manmade images and can be found in many contexts, such as faces, animals, architecture, and patterns. The human visual system quickly detects symmetries and uses them as indicators of salience, ﬁgure-ground organization, and aesthetic preference [1–3] . Turning that percept into a number (a scalar quantifying how symmetric an image is about a given axis, or equivalently how much it departs from symmetry) underpins applications from the quantiﬁcation of anatomical asymmetry in medical imaging [4,5] and of developmental asymmetry in biology [6] to visual aesthetics and design [7,8] . Two distinct problems are often conﬂated under “symmetry”. Detection localizes the symmetry axis (or axes) in an image; scoring (or discrimination) quantiﬁes how symmetric the content is about a given axis. The two are not interchangeable: a detector answers where a symmetry is, whereas a scorer answers how much symmetry there is about a speciﬁed axis, which is the quantity the applications above actually consume. This paper concerns symmetry scoring. Throughout many ﬁelds a variety of scoring methods have been proposed, mostly crafted for a speciﬁc purpose and targeting a speciﬁc application or dataset. They range from hand-crafted measures built on gradients [9], ﬁlter banks [10], frequency coefﬁcients [11], or pixel correlations [7], to more recent measures read from deep-network features [12] . Yet for all this variety, symmetry-scoring methods have never been compared head to head on the same everyday images, under a common protocol with signiﬁcance testing. The primary question of this paper is therefore practical: which of the proposed methods measures mirror symmetry well—and at what computational cost? Answering it also addresses, for the methods that exist today, a second question that the ﬁeld’s drift toward learned features keeps raising: whether reading symmetry from frozen pretrained features earns its cost over classical descriptors. Our contributions are as follows: 1. The ﬁrst benchmark of symmetry scoring, with a uniﬁed open libra

FAQs

What problem does the paper address: symmetry detection or symmetry scoring?

The paper focuses on symmetry scoring, which quantifies how symmetric an image is about a specified axis. Detection and scoring are treated as distinct tasks and are not interchangeable.

How many symmetry scoring methods does the benchmark evaluate?

The benchmark evaluates 13 symmetry scoring methods, with nine collected from prior literature and four introduced in the paper.

What computational insight does the paper report when comparing classical and deep methods?

A tuned classical HOG method trails the best frozen deep-feature readout by only a small but significant margin and runs about 300× faster on CPU, indicating limited added value from frozen deep features for symmetry measurement in the tested setup.

Jul 16, 2026

Upload by Aurelia