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Automatic analysis of artistic paintings using information-based measures

Jorge Miguel Silva, Diogo Pratas, Rui Antunes, Sérgio Matos, Armando J. Pinho

arXiv:2102.01767v1cs.CVcs.ITcs.LGmath.IT

TL;DR

Automatic analysis can support painting authentication and classification, while information in paintings is difficult to quantify. The paper applies Normalized Compression and the Block Decomposition Method, then reports that complexity measures characterize painting styles and artists, with local fingerprints describing how artists distribute information across the canvas.

  • Problem

    The paper asks how to quantify information in paintings and use it to characterize artists and styles, in a setting where automatic analysis supports but does not replace human experts.

    Source: Introduction · p. 1

  • Method

    The authors compare Normalized Compression and the Block Decomposition Method, combine NC with roughness, and construct artist fingerprints from local complexity.

    Source: Introduction · p. 2, Local complexity of paintings · p. 11

  • Results

    NC and roughness confine styles to distinct regions, while local-complexity fingerprints describe artists’ average distribution of information across the canvas.

    Source: Discussion · p. 15

  • Takeaways & Limitations

    Regional complexity and roughness are useful auxiliary features for improving painting style and artist classification.

    Source: Conclusions · p. 16

    The paintings were converted to monochrome, so the influence of color channels remains unexamined in this study.

    Source: Conclusions · p. 16

Abstract

from arXiv · show

The artistic community is increasingly relying on automatic computational analysis for authentication and classification of artistic paintings. In this paper, we identify hidden patterns and relationships present in artistic paintings by analysing their complexity, a measure that quantifies the sum of characteristics of an object. Specifically, we apply Normalized Compression (NC) and the Block Decomposition Method (BDM) to a dataset of 4,266 paintings from 91 authors and examine the potential of these information-based measures as descriptors of artistic paintings. Both measures consistently described the equivalent types of paintings, authors, and artistic movements. Moreover, combining the NC with a measure of the roughness of the paintings creates an efficient stylistic descriptor. Furthermore, by quantifying the local information of each painting, we define a fingerprint that describes critical information regarding the artists' style, their artistic influences, and shared techniques. More fundamentally, this information describes how each author typically composes and distributes the elements across the canvas and, therefore, how their work is perceived. Finally, we demonstrate that regional complexity and two-point height difference correlation function are useful auxiliary features that improve current methodologies in style and author classification of artistic paintings. The whole study is supported by an extensive website (http://panther.web.ua.pt) for fast author characterization and authentication.

Introduction

The paper asks how information in paintings can be quantified and used to characterize artists, styles, and relationships. It compares information-based measures and develops style descriptors and local-complexity fingerprints, with potential use in classification and authentication.

Introduction

  • The paper situates its work in automatic painting analysis, which supports authentication but does not fully replace human experts.It frames information quantification as a way to study how artists expose information and relate to one another.Source: Introduction · pp. 1–2
  • The authors compare unsupervised probabilistic and algorithmic information measures to assess their strengths and weaknesses for analyzing paintings.They frame the study around identifying hidden patterns and relationships through complexity.Source: Introduction · p. 2
  • They combine Normalized Compression (NC) with painting roughness to form a stylistic descriptor.The paper identifies this combination as an efficient way to represent artistic styles.Source: Introduction · p. 2
  • Average local complexity is presented as a fingerprint of how authors compose and distribute elements across the canvas, and how their work is perceived.The paper also describes the fingerprint as capturing artistic influences and shared techniques.Source: Introduction · p. 2
  • The authors propose using information-based measures as auxiliary features to improve existing painting-classification methodologies.The proposed applications include artist authentication, style categorization, organization, and content explanation.Source: Introduction · pp. 1–2

Related Work

Related work motivates automatic measurement of image information and reviews probabilistic and algorithmic approximations, compression methods, and painting-analysis approaches. The methods section introduces the paper’s measures and local-complexity procedure.

Related Work

  • Image information is defined as the smallest number of bits a model needs to represent an image losslessly, using pixel-pattern similarities without exogenous information.The cited background distinguishes combinatorial, probabilistic, and algorithmic approaches; Kolmogorov complexity is non-computable and must be approximated.Source: Related Work · p. 2
  • Lossless compressors vary in their modeling: many target simple statistical regularities, while GeCo and PAQ8 combine multiple models and subprograms.The background also connects compression with minimal description length and algorithmic probability.Source: Related Work · p. 3
  • Painting analysis has used statistical features and models, while CNN-based representations have been proposed for author and style classification.Examples include fractal, wavelet, stroke, and entropy-based analysis, alongside Gram-matrix features from pretrained CNNs.Source: Related Work · p. 3

Methods; 0.1. Information-based measures

  • The methods section describes Normalized Compression and two BDM normalizations, then applies local NC to build author complexity matrices and a distance matrix and phylogenetic tree.The paper also introduces a non-information-based roughness measure.Source: Methods · p. 3, §0.1 · p. 3

two-point height difference correlation function.

Normalized Compression (NC) estimates image information through compressed size, while the Block Decomposition Method (BDM) estimates local algorithmic information using small Turing machines. The paper compares NC with two BDM normalizations, including one scaled by object length and another using minimum- and maximum-complexity reference objects.

Normalized Compression (NC)

  • NC uses an efficient compressor to approximate probabilistic-algorithmic information, with compressed size normalized by input length for size-independent comparisons.For binary images, the alphabet size is 2.Source: Normalized Compression (NC) · pp. 3–4

Normalized Block Decomposition Method (NBDM)

  • BDM uses small Turing machines to estimate local algorithmic information, falling back to Shannon entropy when accuracy is lost.NBDM1 normalizes BDM by the digital object's length for direct comparison with NC.Source: Normalized Block Decomposition Method… · p. 4
  • NBDM2 uses minimum- and maximum-complexity reference objects, with the maximum object covering high-CTM slices before repeating them.The normalization aims to remove the constant factor associated with the choice of description language.Source: Normalized Block Decomposition Method… · p. 4

Local complexity analysis using the Normalized Compression

The paper measures local painting complexity with NC in image patches and compares authors through their average complexity patterns. It also estimates brightness contrast using the two-point height difference correlation function and derives a roughness exponent from its curve.

Local complexity analysis using the Normalized Compression

  • Images were divided into 16x16 blocks, producing 256 regional NC values per painting; patch sizes of 8x8 and 32x32 were also tested.Per-author average complexity matrices were formed from the paintings' matrices.Source: Local complexity analysis using the… · p. 5
  • Distances between authors' average complexity matrices formed a similarity matrix used to build phylogenetic trees with UPGMA and Kruskal's minimum spanning tree algorithm.The matrix distance uses absolute differences between corresponding complexity values.Source: Local complexity analysis using the… · p. 5

0.2. Two-point height di

  • The two-point height difference correlation function quantifies brightness contrast, and its roughness exponent is the slope of its double-logarithmic curve.The slope runs from r_initial = 10 to the saturation point, approximately 30% of image width.Source: §0.2 · p. 5

Assessment pipeline

The assessment pipeline standardizes painting images before applying NC and two BDM normalizations. PAQ8 was selected as the compressor because it achieved the best compression ratio on the processed painting dataset, despite higher resource demands.

Assessment pipeline

  • The pipeline converts dataset images to PGM, quantizes them to 8 bits with Lloyd-Max, binarizes them to ASCII 01, then applies NC, NBDM1, and NBDM2.Binarization is used because BDM supports only a small alphabet.Source: Assessment pipeline · p. 5

Finding an effective data compressor

  • Seven compressors were compared, and PAQ8 was used to compress each quantized image despite its greater resource use.The authors considered the cost acceptable for approximating the bits needed to reproduce each image.Source: Finding an effective data compressor · pp. 5–6
  • PAQ8 achieved the best compression ratio on the processed painting dataset, improving by approximately 26% over XZ.Figure 1 compares total bytes when each image is compressed individually; PAQ8 requires more RAM and computation time.Source: Finding an effective data compressor · p. 5, Figure 1 · p. 6

Results

Tests show different strengths and limitations for NC and BDM: NC is more robust than NBDM1 to pixel edits, while BDM can identify simple algorithmic image structure. A super-sampling transformation also exposes a case where BDM sharply underestimates information, motivating the paper's combined use of NC and NBDM.

Comparison of NC and BDM

  • With the same normalization, NC was more robust than NBDM1 as pseudo-random pixel edits increased; NBDM2 was more robust than NBDM1.The test used 50 edited copies per painting, with edit rates from 1% to 50%, across paintings by three authors.Source: Comparison of NC and BDM · p. 6, Figure 2 · p. 7
  • BDM assigns minimal values to simple algorithmic outputs such as cellular automata, which compressors have difficulty compressing.Most tested datasets showed similar NC and NBDM1 behavior, with cellular automata and CR images as exceptions.Source: Comparison of NC and BDM · pp. 6–7, Figure 2 · p. 7
  • Super-sampling each binary character into a 4x4 block reduced measured BDM from 370981 bits to 79 bits, exposing underestimation.The transformed blocks match BDM's default 4x4 block size, so uniform blocks receive approximately zero complexity.Source: Comparison of NC and BDM · p. 7, Figure 2 · p. 7

Information-based measures in images of artistic paintings

Global measures analysis

Painting complexity ranges from simple abstract patterns to irregular, detailed compositions, while combining NC with HDC roughness separates most styles more effectively than either measure alone.

Global measures analysis

  • Low-complexity paintings tend toward abstract, minimalist patterns; the most complex are irregular, detailed, and convoluted.At intermediate complexity, detailed regions often appear against lower-complexity backgrounds, a pattern associated with chiaroscuro.Source: Global measures analysis · p. 8, Figure 3 · p. 8
  • Author rankings shift by 13.4 ± 11.37 positions for NBDM1 and 4.9 ± 4.3 for NC across quantizations.The analysis compared 4-, 6-, and 8-bit quantizations; NBDM1 rankings varied more than NC rankings.Source: Global measures analysis · pp. 8–9, Figure 4 · p. 9
  • Both measures place minimalist artists and movements toward the low-complexity end, and detailed artists toward the high end.Abstract Expressionism appears at both extremes: Pollock’s values are near random, while Rothko’s Color Field work is low-complexity.Source: Global measures analysis · pp. 9–10

Combining the NC with the roughness exponent of HDC function

  • Combined NC and HDC roughness confine styles to distinct regions, except Abstract Expressionism, where the measures vary inversely.NC contributes average painting information, while HDC roughness captures brightness and relative spatial position.Source: Combining the NC with the roughness… · p. 10, Figure 5 · p. 10

Local complexity of paintings

Local complexity matrices summarize where artists typically place detail across the canvas, and distances between these fingerprints organize artists by movement and possible influence.

Local complexity of paintings

  • The 16×16-block fingerprints capture each artist’s average range of complexity and where detail is concentrated across the canvas.The study reports 16×16 as the minimum tested patch size at which compression-rate differences were noticeable; 8×8 and 32×32 blocks were also tested.Source: Local complexity of paintings · p. 11, Figure 6 · p. 11
  • Artists’ fingerprints differ in spatial emphasis: some distribute high complexity broadly, while others concentrate it centrally or near the borders.Pollock and Johns show dispersed high complexity; Bacon and de la Tour emphasize the center, while Rothko and Mondrian emphasize borders.Source: Local complexity of paintings · p. 11, Figure 6 · p. 11
  • Fingerprint-based trees group artists from several shared movements and show some cross-movement relationships interpreted as artistic influences.Reported groupings include Renaissance, Baroque, Romanticists, Impressionists, Surrealism, Cubism, and Abstract Expressionism.Source: Local complexity of paintings · pp. 12–13, Figure 7 · p. 12
  • Tree relationships may be affected by region count or the similarity and tree-building algorithms, although Kruskal’s tree produced similar results to UPGMA.The authors also suggest that proximity can reflect compositional approaches beyond period, movement, or influence.Source: Local complexity of paintings · pp. 11–13
  • The authors conclude that local complexity fingerprints describe style, influence, and how artists project their work onto the canvas.They connect regional complexity to composition and other features involved in how a work is perceived.Source: Local complexity of paintings · p. 13

Evaluation of measures for classification purposes

The evaluation finds that regional complexity and HDC improve classification when added to the baseline, while the discussion shows how NC, BDM, and local complexity characterize paintings and artists. NC and roughness also distinguish artistic styles, and author fingerprints capture patterns of composition and artistic relationships.

Evaluation of measures for classification purposes

  • 2.8 p.p. in style accuracy and 2.0 p.p. in author accuracy were gained by adding HDC and regional complexity to the baseline ensemble.The table reports test-set accuracy for the baseline, baseline with regional complexity, and an ensemble with regional complexity and HDC.Source: Table 1 · p. 14, Evaluation of measures for… · p. 14
  • Regional complexity alone increased accuracy by 2.2 p.p. for style and 1.0 p.p. for author classification, with greater impact than HDC.The authors relate the combined-feature gains to handcrafted and non-handcrafted features extracting different information.Source: Evaluation of measures for… · p. 14

Discussion

  • NC was more robust than BDM to uniform pixel editing, while BDM's blockwise design misses information shared between blocks and can underestimate complexity after supersampling.The authors also found NC and NBDM results similar across image types except computed radiography and cellular automata, where BDM captured algorithmic structure that the compressor did not.Source: Discussion · p. 14
  • Low-complexity paintings were often abstract, minimalist, or patterned, while the most complex were globally irregular, detailed, and convoluted.Jackson Pollock's average complexity was close to random; the authors note this may relate to symbolic layers and dispersion across the canvas.Source: Discussion · p. 15
  • Combining NC with the HDC roughness exponent confined styles to distinct regions; Colour Field artists had high α and low NC, while Action Painting artists showed the opposite.The authors describe NC as adding average information to the brightness and relative spatial position represented by the roughness exponent.Source: Discussion · p. 15
  • Average regional-complexity fingerprints describe where artists place detail and emphasis, while distance-based trees group same-style artists and reveal influence or shared techniques.The authors give Holbein and Vermeer as an example of proximity associated with shared use of optics despite different styles.Source: Discussion · p. 15

Conclusions

The conclusions present NC and BDM as complementary information measures for painting analysis, with fingerprints and regional complexity useful for describing artists and improving classification. The study analyzes monochrome images and identifies color-channel analysis as a future direction.

Conclusions

  • NC is more robust to pixel edits and quantization, whereas BDM can identify data resembling simple algorithms but struggles with block-based full-information quantification.The conclusions describe NC, particularly when combined with roughness exponent α, as a stylistic descriptor and fingerprints as representations of typical content distribution across an artist's canvas.Source: Conclusions · p. 16
  • Regional complexity and HDC are useful auxiliary features for improving current author and style classification methods.Fingerprints are also described as useful for art content explanation, authorship attribution, validation, and relating artists through stylistic influences and shared techniques.Source: Conclusions · p. 16
  • The analysis used monochrome paintings; the authors suggest separating color channels to study color's influence on complexity.Other proposed directions include separating fingerprint characteristics and using a competitive compressor to select a model for each painting or region.Source: Conclusions · p. 16

Website

  • The supporting website presents the study pipeline, author measures, fingerprints, paintings, and phylogenetic trees.It also provides a magnifier for closer inspection of the trees.Source: Website · p. 16

A. Supplement

The supplement reports little effect of image normalization on the measures, including regional-complexity distances. It also compares fingerprint block sizes and identifies 16×16 as a balance between detail and differentiation.

A.1. Comparison towards normalized images

  • Normalization had low average variation and percentage differences across measures, with NBDM most affected and roughness exponent α least affected.The authors conclude normalization did not significantly affect the measures.Source: §A.1 · p. 20, Table S1 · p. 20
  • 0.955 correlation (p-value 0.001) and an average distance difference of 3.2622 ± 2.820 support the authors' conclusion that regional-complexity distances are robust to normalization.The Mantel test compares the normalized and non-normalized distance matrices.Source: §A.1 · p. 20, Table S2 · p. 22

A.2. Comparison towards other fingerprints

  • For regional complexity, 8x8 and 16x16 images were divided into equally numbered tiles of slightly different sizes, while 32x32 used same-sized blocks except for remainders when dimensions were not exact multiples.Source: §A.2 · p. 20
  • 16×16 fingerprints balance detail and differentiation: distance correlations were 0.951 for 8×8 versus 16×16 and 0.918 for 16×16 versus 32×32.The figure's heat maps show each author's complexity range and where they paint with more detail; patterns became less noticeable at 32×32.Source: §A.2 · pp. 21–22, Figure S1 · p. 21, Table S2 · p. 22

A.3. Average NBDM2 per Artist

The supplement reports limited positional variation for NBDM2 across quantizations and checks the UPGMA tree using a Kruskal minimum spanning tree. The resulting tree retains reported influence links and groups some artists from the same movements.

A.3. Average NBDM2 per Artist

  • 13.2 ± 13.2 was the average relative positional variation between authors for NBDM2 across quantizations.The authors report higher average standard deviation than for NBDM1, but conclude normalization has minimal impact on NBDM2 results.Source: §A.3 · p. 22

A.4. Kruskal minimum spanning tree

  • The Kruskal minimum spanning tree retained the UPGMA tree's author connections despite a different, sparser arrangement.The authors constructed it to verify the congruence of the UPGMA tree.Source: §A.4 · p. 22
  • The minimum spanning tree preserved influence links across movements and grouped some artists from the same movements, supporting fingerprints as qualitative descriptions of painting style.Examples of cross-movement links include Titian with Diego Velazquez and Caravaggio with Francisco de Zurbarán.Source: §A.4 · p. 22

A.5. Replication of Results

The repository provides Linux scripts for reproducing the study’s dataset preparation, measurements, benchmarks, analyses, and visualizations. Separate workflows cover information-measure assessment and application to paintings.

A.5. Replication of Results

  • The repository scripts support full replication under Linux, including tool installation, dataset download, assessment, benchmarking, measurement, and visualization.The overview also gives the initial commands for granting script execution access and starting automatic installation.Source: §A.5 · p. 22

A.5.1. Information-based Measures Assessment

  • Assessment scripts prepare the dataset, run compression benchmarks, compare NC and NBDM variants, test pixel substitutions and diverse images, and reproduce cellular-automata and BDM-underestimation experiments.Figure S2 presents authors’ average NBDM2 values for 4-, 6-, and 8-bit quantization, sorted by value.Source: §A.5.1 · pp. 22–23, Figure S2 · p. 23

A.5.2. Information-based measures applied to artistic paintings

  • Painting-analysis scripts run the pipeline, quantize and preprocess images, calculate per-author average complexities, and reproduce HDC, regional-complexity, fingerprint, distance-matrix, tree, and classification analyses.The author and style classifications have separate notebooks; Figure S3 shows an artists’ tree computed using a Kruskal minimum spanning tree.Source: §A.5.2 · pp. 23–24, Figure S3 · p. 24
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