Adaptive Radial Projection on Fourier Magnitude Spectrum for Document Image Skew Estimation

Luan Pham; Phu Hao Hoang; Xuan Toan Mai; Tuan Anh Tran

cs.CVMar 6, 2026

Adaptive Radial Projection on Fourier Magnitude Spectrum for Document Image Skew Estimation

Authors: Luan Pham, Phu Hao Hoang, Xuan Toan Mai, Tuan Anh Tran

Organizations: Cinnamon AI - Department of Research, Floor 10th, No. 36 Hoang Cau street, O Cho Dua Ward, Dong Da District, Hanoi City, Viet Nam. · Faculty of Computer Science & Engineering, Ho Chi Minh City-University of Technology (HCMUT), 268 Ly Thuet Street, District 10, Ho Chi Minh City, Vietnam · Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam.

Abstract

Skew estimation is one of the vital tasks in document processing systems, especially for scanned document images, because its performance impacts subsequent steps directly. Over the years, an enormous number of researches focus on this challenging problem in the rise of digitization age. In this research, we first propose a novel skew estimation method that extracts the dominant skew angle of the given document image by applying an Adaptive Radial Projection on the 2D Discrete Fourier Magnitude spectrum. Second, we introduce a high quality skew estimation dataset DISE-2021 to assess the performance of different estimators. Finally, we provide comprehensive analyses that focus on multiple improvement aspects of Fourier-based methods. Our results show that the proposed method is robust, reliable, and outperforms all compared methods. The source code is available at https://github.com/phamquiluan/jdeskew.

Figures & tables

Figure 1: The overview of our adaptive projection.

Panel of Figure 2 — Figure 2: The change of AED and CE levels when tuning the distance $\mathcal{D}$ . The chosen threshold ( x ) should bring the lowest AED value.

Panel of Figure 3 — Figure 3: An example of low-quality annotation in DISEC2013, deskewed by DISEC2013 ground-truth angle (left) and our system (right).

Block Size	1024			2048
Block Size	AED	TOP80	CE	AED	TOP80	CE
$N=h*0.1$	0.95	0.75	0.01	0.91	0.55	0.03
$N=h*0.2$	0.56	0.43	0.03	0.51	0.33	0.02
…	…	…	…	…	…	…
$N=h*0.9$	0.16	0.11	0.39	0.15	0.08	0.57
$N=h$	0.14	0.09	0.47	0.12	0.07	0.62

Table 1: Effects of image division with different block size.

	1024			2048
	AED	TOP80	CE	AED	TOP80	CE
Magnitude Spectrum	0.14	0.09	0.47	0.12	0.07	0.62
Power Spectrum	0.2	0.14	0.28	0.19	0.15	0.35

Table 2: Comparison of Magnitude and Power Spectrum

Window Size	1024			3072
Window Size	AED	TOP80	CE	AED	TOP80	CE
$W=15$	0.14	0.09	0.47	0.1	0.06	0.68
$W=35$	0.13	0.09	0.49	0.1	0.06	0.69
$W=55$	0.13	0.09	0.51	0.11	0.06	0.7
$W=75$	0.13	0.09	0.53	0.11	0.06	0.72
$W=h/10$	0.13	0.08	0.55	0.74	0.04	0.81

Table 3: Efficiency comparison when discarding the DC component and small frequencies by different window size on our baseline.

Panel of Figure 4 — Figure 4: (a) The sorted absolute error curve and (b) its log-scale version of four different methods on DISE 2021 ( $15^{\circ}$ ) dataset.

Method	DISE 2021				DISE 2021 (45)
Method	AED	TOP80	CE	WE	AED	TOP80	CE	WE
Our (2048)	0.08	0.04	0.84	1.13	0.06	0.03	0.87	1.06
Our (3072)	0.07	0.04	0.86	1.13	0.06	0.02	0.88	1.06
Our (4096)	0.08	0.04	0.83	1.18	0.06	0.03	0.86	1.06
FredsDeskew	10.82	0.09	0.54	109	12.44	0.1	0.51	110
PypiDeskew	16.59	0.24	0.2	141	21.79	2.51	0.14	179

Table 4: Quantitative comparison of different methods on the DISE2021

15^{\circ}

and

44.9^{\circ}

datasets.

Document Image Understanding

Document image understanding turns page images into recognized text, layout, structured data, and answers grounded in visual evidence.

See all 148 papers

Alignment of Similarity-Transformed Images Based on Fourier--Mellin Transform Using Auxiliary Function Method
Aug 12, 2026Shinji Yamashita, Yuma Kinoshita, Hitoshi KiyaImage Matching
Tokai University, Japan · Tokyo Metropolitan University, Japan
Implementation and discussion of the Pith Estimation on Rough Log End Images using Local Fourier Spectrum Analysis method
Mar 14, 2026Henry Marichal, Diego Passarella, Gregory Randall
Instituto de Ingenieria Electrica, Facultad de Ingenieria, Universidad de la Republica, Uruguay · Sede Tacuarembo, CENUR Noreste, Universidad de la Republica, Uruguay
Sliced Wasserstein Sketches with Error Certificates
Oct 14, 2026Elaheh Akbari, James Liu, Keaton Hamm +1Sliced Wasserstein Distance Vector Quantization
College of Connected Computing, Vanderbilt University · Department of Mathematics, Division of Data Science, University of Texas at Arlington

Aug 12, 2026J/K move · Enter open · S save

Alignment of Similarity-Transformed Images Based on Fourier--Mellin Transform Using Auxiliary Function Method

Shinji Yamashita, Yuma Kinoshita, Hitoshi Kiya

Tokai University, Japan · Tokyo Metropolitan University, Japan

Image Matching

Open paper AskPDF arXiv

This paper proposes an algorithm for estimating the similarity transformation, namely translation, scale, and rotation, between two images with subpixel accuracy. Image registration is a fundamental technique for aligning images acquired under different viewpoints and imaging conditions, and a representative approach based on maximizing discrete cross-correlation is the Fourier--Mellin registration. However, the Fourier--Mellin approach often fails to achieve sufficient alignment accuracy when subpixel-level estimation is required. The proposed method integrates (i) scale-and-rotation estimation from the Fourier magnitude spectrum in a log-polar representation and (ii) maximization of phase-only correlation based on the auxiliary function method. This integration enables a two-stage estimation procedure: it first estimates scale and rotation without being affected by translation, and then estimates translation with subpixel precision in the spatial domain using the corrected image pair. A simulation experiment on image pairs subjected to random similarity transformations demonstrates that the proposed method reduces estimation errors in scale, rotation, and translation compared with Fourier--Mellin-based registration methods using discrete cross-correlation.

Abstract

Document Image Understanding

Explore similar work

Alignment of Similarity-Transformed Images Based on Fourier--Mellin Transform Using Auxiliary Function Method

Implementation and discussion of the Pith Estimation on Rough Log End Images using Local Fourier Spectrum Analysis method

Sliced Wasserstein Sketches with Error Certificates