Contour and Texture Analysis for Image Segmentation

J. MalikSerge J. BelongieThomas K. LeungJianbo Shi

article2001IJCV1,375 citations

Proposes a unified image segmentation framework that combines intervening contour cues and texton-based texture analysis through an adaptive gating mechanism within the normalized cuts graph-partitioning algorithm.

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Natural image interpretation in computer vision fundamentally depends on segmenting scenes into coherent regions and objects. Historically, automated segmentation systems have treated contour detection and texture analysis in isolation. This separation causes significant errors: edge detectors generate dense, misleading webs of false boundaries in textured areas, while texture models frequently misclassify sharp image boundaries as distinct textural bands. The article develops and evaluates a unified grayscale image segmentation framework that simultaneously integrates contour and texture cues to produce coherent, disjoint image regions across complex, natural scenes.

To achieve robust cue integration, the article transforms image patches into discrete visual prototypes called "textons" by clustering filter responses from a multi-scale, multi-orientation filter bank. Texture scale is automatically determined from the spatial distribution of these textons, and local texture differences are measured using windowed texton histograms. To prevent mutual interference between cues, the algorithm introduces a local "gated" mechanism based on surrounding texturedness: it suppresses contour responses inside textured regions and excludes boundary edges from polluting texture histograms. These combined similarity cues define a sparse graph of pixel relationships, which is globally partitioned using the spectral graph-theoretic framework of normalized cuts through an iterative over-segmentation and graph-coarsening strategy.

Key findings show that the unified gating mechanism successfully prevents false edge responses within textures while preserving low-contrast, perceptually salient object boundaries. Across a broad test set of over 1,000 diverse natural images—including animals, people, outdoor scenes, and artwork—the algorithm achieved clean, accurate segmentations using a single, fixed set of parameters without manual tuning. Furthermore, graph coarsening reduced the computational complexity of the global partitioning step substantially, enabling execution times of under two minutes per image on standard hardware.

These results demonstrate that multi-cue integration is critical for practical computer vision, offering a dependable foundation for downstream recognition and visual processing tasks without requiring fragile parameter customization for different image types. The article recommends utilizing this unified framework for general image partitioning and notes that performance can be directly extended by incorporating color cues. As next steps, the authors highlight the need to develop standardized ground-truth benchmark datasets for objective evaluation and explore adaptive methods for choosing the optimal texton vocabulary size, noting that formal benchmarking remains an ongoing area of research.

Carnegie Mellon University Compaq Cambridge Research Laboratory Computer Science Division University of California Berkeley computer hardware computer vision edge detectors image segmentation texture analysis edge detection

Malik et al (2001).pdf

Paper: Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation, Song Chun Zhu et al. (1996). It provides foundational statistical principles for integrating region properties with boundary competition that motivate the unified contour and texture framework.
Paper: Markov Random Field Texture Models, G. R. Cross et al. (1983). It establishes essential early statistical modeling of spatial texture interactions that informs local filter responses and texton representations.

Paper: Contour Detection and Hierarchical Image Segmentation, Pablo Arbeláez et al. (2011). It directly advances the contour and texture gradient integration and spectral partitioning concepts to establish the generalized global Probability of Boundary (gPb) hierarchical segmentation benchmark.
Paper: Blobworld: Image Segmentation Using Expectation-Maximization and Its Application to Image Querying, C. Carson et al. (2002). It applies the integrated texture-scale and color segmentation principles developed by the same research group directly to region-based image querying and retrieval.
Paper: TextonBoost: Joint Appearance, Shape and Context Modeling for Multi-class Object Recognition and Segmentation, J. Shotton et al. (2006). It builds upon the concept of texton distributions by combining texton maps with discriminative boosting in a conditional random field for joint recognition and semantic segmentation.
Paper: Efficient Graph-Based Image Segmentation, PEDRO F. FELZENSZWALB et al. (2004). It introduces a fast, alternative graph-based partitioning predicate that provides a computationally efficient counterpart to normalized cut segmentation.
Paper: Selective Search for Object Recognition, Jasper R. R. Uijlings et al. (2013). It uses bottom-up hierarchical region merging across diverse color and texture cues as an object proposal generator for recognition pipelines.
Paper: SLIC Superpixels Compared to State-of-the-Art Superpixel Methods, Radhakrishna Achanta et al. (2012). It builds on modern segmentation and boundary adherence needs by developing a highly efficient local clustering approach for superpixel generation.
Paper: "GrabCut": interactive foreground extraction using iterated graph cuts, Carsten Rother et al. (2004). It extends graph-based energy minimization and iterative boundary optimization to user-guided interactive foreground extraction.
Paper: Mean Shift: A Robust Approach Toward Feature Space Analysis, Dorin Comaniciu et al. (2002). It presents a prominent non-parametric feature-space alternative for joint spatial-color-texture image smoothing and segmentation.

Cover for Contour and Texture Analysis for Image Segmentation

Abstract

This paper provides an algorithm for partitioning grayscale images into disjoint regions of coherent brightness and texture. Natural images contain both textured and untextured regions, so the cues of contour and texture differences are exploited simultaneously. Contours are treated in the intervening contour framework, while texture is analyzed using textons. Each of these cues has a domain of applicability, so to facilitate cue combination we introduce a gating operator based on the texturedness of the neighborhood at a pixel. Having obtained a local measure of how likely two nearby pixels are to belong to the same region, we use the spectral graph theoretic framework of normalized cuts to find partitions of the image into regions of coherent texture and brightness. Experimental results on a wide range of images are shown.

Topics

computer hardware computer vision edge detectors filter banks image patches local feature local texture normalized cuts over segmentation test samples

Keywords

image segmentation texture analysis edge detection contour orientation texture descriptor contour energy texturedness measure texture perception

1. Introduction
1.1. Desiderata of a Theory of Image Segmentation
1.2. Introducing Textons
1.3. Summary of Our Approach
2. Filters, Composite Edgels, and Textons
2.1. Textons
3. The Normalized Cut Framework
4. Defining the Weights
4.1. Images Without Texture
4.2. Images that are Texture Mosaics
4.3. General Images
5. Computing the Segmentation
5.1. Computing the Initial Segmentation
5.2. Updating Weights
5.3. Coarsening the Graph
5.4. Computing the Final Segmentation
5.5. Segmentation in Windows
6. Results
7. Conclusion
Acknowledgments
Notes
References

Knowls

Knowl 1 — Texton Generation and Filter Bank Architecture
model/method
Textures are characterized by mapping image patches to discrete prototypes called textons, obtained by vector quantizing linear spatial filter outputs across the image.

The front-end filter bank contains $N_{\text{fil}} = 40$ filters consisting of:
1. Oriented quadrature filter pairs (36 filters): Even-symmetric second Gaussian derivatives and their odd-symmetric Hilbert transforms along the $y$ -axis, defined at 3 scales (spaced by half-octaves), 6 orientations equally spaced in $[0, \pi)$ , and an aspect ratio (elongation) of $\ell = 3$ : $f_1(x, y) = \frac{d^2}{dy^2} \left( \frac{1}{C} \exp\left(-\frac{y^2}{\sigma^2}\right) \exp\left(-\frac{x^2}{\ell^2 \sigma^2}\right) \right)$ $f_2(x, y) = \text{Hilbert}(f_1(x, y))$ where $\sigma$ is scale and $C$ is a normalization constant.
2. Center-surround filters (4 filters): Radially symmetric Difference-of-Gaussians (DoG) kernels at 4 scales.
All filter kernels are zero-mean and $L_1$ -normalized for scale invariance. At each pixel $x$ , the filter response vector $F(x) \in \mathbb{R}^{40}$ is contrast-normalized according to Weber's law: $F(x) \leftarrow F(x) \cdot \frac{\log\left(1 + \frac{\|F(x)\|_2}{0.03}\right)}{\|F(x)\|_2}$

The normalized filter vectors across the image are clustered into $K = 36$ prototype centers using $K$ -means. Each pixel is assigned to its nearest cluster center $T(x) \in \{1, \dots, K\}$ , partitioning the image into $K$ discrete texton channels.
Knowl 2 — Texturedness Gating Operator for Cue Combination
model/method
To combine contour and texture cues without generating false contours inside textured regions or false texture boundaries along step edges, a local texturedness gating operator $p_{\text{texture}}$ is evaluated at contour energy peaks.

Contour orientation energy $OE_\theta$ is computed via quadrature pairs: $OE_\theta = (I * f_{1,\theta})^2 + (I * f_{2,\theta})^2$ At each pixel $q$ , the dominant orientation $\theta^* = \arg\max_\theta OE_\theta$ and maximum energy $OE^*$ are identified. Applying non-maximal suppression along the normal to $\theta^*$ yields composite edgels with raw contour probability: $p_{\text{con}}(q) = 1 - \exp(-OE^*(q) / \sigma_{\text{IC}})$ where $\sigma_{\text{IC}} = 0.02$ .

For each edgel $q$ with local scale $\alpha(q)$ , a circular window of radius $\alpha(q)$ centered at $q$ is partitioned along the diameter tangent to $\theta^*$ into three regions: a central thin strip $D_0$ , a left half $D_-$ , and a right half $D_+$ . The $\chi^2$ distance between $K$ -bin texton histograms is computed under two partitionings: $\chi^2(h_L, h_R) = \frac{1}{2} \sum_{k=1}^K \frac{(h_L(k) - h_R(k))^2}{h_L(k) + h_R(k)}$ where $h_L$ and $h_R$ are evaluated for $(D_0 \cup D_-, D_+)$ and $(D_-, D_0 \cup D_+)$ , and the maximum is retained as $\chi^2_{\text{LR}} = \max\{\chi^2(h_{D_0 \cup D_-}, h_{D_+}), \chi^2(h_{D_-}, h_{D_0 \cup D_+})\}$ .

The local texturedness probability $p_{\text{texture}}(q)$ is computed via a sigmoid function: $p_{\text{texture}}(q) = 1 - \frac{1}{1 + \exp\left(-\frac{\chi^2_{\text{LR}} - \tau}{\beta}\right)}$ with parameters $\tau = 0.3$ and $\beta = 0.04$ . For pixels that are not orientation energy maxima, $p_{\text{texture}}$ is defined to be $0$ . The gated contour boundary probability $p_B$ is defined as: $p_B(q) = (1 - p_{\text{texture}}(q)) \cdot p_{\text{con}}(q)$
Knowl 3 — Gated Pairwise Affinity Metric Combining Contour and Texture
model/method
The pairwise similarity weight $W_{ij}$ between pixels $i$ and $j$ combines intervening contour cues and texton histogram differences using texturedness gating: $W_{ij} = W_{ij}^{\text{IC}} \times W_{ij}^{\text{TX}}$
1. Gated Intervening Contour Affinity ( $W_{ij}^{\text{IC}}$ ): $W_{ij}^{\text{IC}} = 1 - \max_{x \in M_{ij}} p_B(x)$ where $M_{ij}$ is the set of local maxima along the straight line segment connecting pixels $i$ and $j$ , and $p_B(x) = (1 - p_{\text{texture}}(x)) p_{\text{con}}(x)$ is the gated boundary probability.
2. Gated Texture Affinity ( $W_{ij}^{\text{TX}}$ ): At each pixel $i$ , a $(K+1)$ -bin histogram $\hat{h}_i$ is computed over an axis-aligned square window $W(i)$ of radius $\alpha(i)$ : $\hat{h}_i(k) = \sum_{j \in \mathcal{N}(i)} p_{\text{texture}}(j) \cdot I[T(j) = k], \quad \forall k \in \{1, \dots, K\}$ $\hat{h}_i(0) = N_B + \sum_{j \in \mathcal{N}(i)} (1 - p_{\text{texture}}(j))$ where $\mathcal{N}(i)$ is the set of oriented energy maxima in $W(i)$ , $T(j)$ is the texton assignment of pixel $j$ , and $N_B$ is the number of pixels in $W(i)$ that are not oriented energy maxima. The affinity is then computed as: $W_{ij}^{\text{TX}} = \exp\left(-\frac{\chi^2(\hat{h}_i, \hat{h}_j)}{\sigma_{\text{TX}}}\right)$ with $\sigma_{\text{TX}} = 0.025$ , where $\chi^2(\hat{h}_i, \hat{h}_j) = \frac{1}{2} \sum_{k=0}^K \frac{(\hat{h}_i(k) - \hat{h}_j(k))^2}{\hat{h}_i(k) + \hat{h}_j(k)}$ .
Knowl 4 — Adaptive Local Texture Scale Selection via Delaunay Triangulation
model/method
Local texture scale $\alpha(i)$ at pixel $i$ is estimated adaptively from the spatial distribution of identical texton assignments using computational geometry:
1. For a pixel $i$ assigned to texton channel $T(i)$ , treat pixel $i$ as a thickened disk of radius $r_{\text{in}}$ (set to 3% of the image dimension, matching the intermediate filter scale).
2. Construct the 2D Delaunay triangulation of all pixels belonging to channel $T(i)$ .
3. Identify all Delaunay neighbors of all pixels in the thickened disk of $i$ that lie within an outer distance bound $r_{\text{out}}$ (set to 10% of the image dimension).
4. Compute the Euclidean distances from each identified neighbor pixel to pixel $i$ .
5. The raw scale $\alpha_{\text{raw}}(i)$ is defined as $1.5$ times the median of these Euclidean distances.
6. Apply 2D median filtering across the resulting $\alpha_{\text{raw}}$ map to produce the smoothed local scale image $\alpha(i)$ .
Knowl 5 — Two-Stage Spectral Graph Partitioning via Graph Coarsening
algorithm
The image segmentation framework computes an initial oversegmentation, refines the pairwise weights within segment boundaries, coarsens the graph into supernodes, and produces the final segmentation via recursive Normalized Cuts.
Input: Image $I$ , texton channels $T$ , scale map $\alpha$
Output: Disjoint partition of image pixels into regions
1. Construct sparse affinity matrix $W \in \mathbb{R}^{N \times N}$ with $W_{ij} = W_{ij}^{\text{IC}} \times W_{ij}^{\text{TX}}$ for pairs with distance $\le 30$ pixels (approx. 1000 connections/pixel).
2. Compute diagonal degree matrix $D$ where $D_{ii} = \sum_j W_{ij}$ .
3. Solve generalized eigensystem $(D - W)v = \lambda D v$ for the 2nd through 12th smallest eigenvectors $v_2, \dots, v_{12}$ and eigenvalues $\lambda_2, \dots, \lambda_{12}$ .
4. Form normalized pixel feature vectors $u(x) = [\frac{v_2(x)}{\sqrt{\lambda_2}}, \dots, \frac{v_{12}(x)}{\sqrt{\lambda_{12}}}]^T \in \mathbb{R}^{11}$ .
5. Cluster $u(x)$ via $K$ -means initialized with $K^* = 30$ centers and baseline RMS error $e^*$ .
6. Greedily remove centers that yield the minimal increase in RMS error until quantization error $e > 1.1 \times e^*$ , yielding initial oversegmentation $S_0 = \{R_1, \dots, R_{N_0}\}$ .
7. Update weights: recompute texton histograms collecting only textons in $R_k \cap W(i)$ for $i \in R_k$ , and set $p_B(x) = 0$ for all $x$ not lying on boundaries of $S_0$ .
8. Coarsen graph into $N_0$ supernodes with weights:
    $\hat{W}_{kl} = \sum_{i \in R_k} \sum_{j \in R_l} W_{ij}$
9. Recursively bipartition the coarsened graph $\hat{W}$ using the second eigenvector of its normalized Laplacian:
   a. Find threshold among 30 candidate values in eigenvector range minimizing $Ncut$ .
   b. Recurse on partitions while minimum $Ncut \le 0.1$ .
return Final partitioned regions
Knowl 6 — Windowed Segmentation Framework for Large Scale Images
model/method
To prevent global Normalized Cuts from missing small or local regions in complex images, segmentation is structured hierarchically across overlapping window quadrants:
1. Quadrant Decomposition: The image domain is divided into four disjoint quadrants $Q_1, Q_2, Q_3, Q_4$ such that $\bigcup_{i=1}^4 Q_i = \text{Image}$ and $Q_i \cap Q_j = \emptyset$ .
2. Margin Expansion: Each quadrant is expanded into an overlapping window $\hat{Q}_i$ by adding a margin $r = \max_x \alpha(x)$ , where $r$ is the maximum estimated local scale across the image.
3. Local Oversegmentation: On each $\hat{Q}_i$ , local weight submatrix $\hat{W}^i$ is formed, and initial oversegmentation $\hat{S}_0^i$ is obtained via spectral clustering. $\hat{S}_0^i$ is cropped to $Q_i$ as $S_0^i$ , and merged across quadrants to obtain full initial oversegmentation $S_0 = \bigcup_{i=1}^4 S_0^i$ .
4. Boundary and Histogram Update: Texton histograms for pixels in $Q_i$ are collected from the full $(2\alpha + 1)^2$ window contained in $\hat{Q}_i$ . Boundary probability $p_B$ is set to zero for all pixels not lying on region boundaries of $\hat{S}_0^i$ .
5. Global Graph Coarsening and Final Cut: Graph coarsening is performed globally across all regions in $S_0$ , and recursive Normalized Cuts bipartitioning is run on the resulting coarsened graph.
Knowl 7 — Empirical Segmentation Performance and Computational Efficiency
empirical result
The combined contour and texture segmentation algorithm was evaluated on over 1000 grayscale natural images from the Corel Stock Photos database, covering categories including animals, portraits, natural landscapes, architectural scenes, and paintings.

Key performance characteristics reported:
- Parameter Robustness: All experimental results across all image categories were generated using a single invariant set of hyperparameters ( $K = 36$ , $\sigma_{\text{IC}} = 0.02$ , $\sigma_{\text{TX}} = 0.025$ , $\tau = 0.3$ , $\beta = 0.04$ , $Ncut$ stopping threshold $= 0.1$ ).
- Computational Speed: A C++ implementation running on a 750 MHz Pentium III machine segments images of size $108 \times 176$ pixels in under two minutes.
- Graph Sparsity: Enforcing a connection radius of 30 pixels with approximately 1000 non-zero connections per pixel maintained computational tractability while preventing boundary leakages.

Coverage note — No substantial contributed material was omitted. The knowls capture the filter bank architecture, texton clustering, adaptive scale selection, texturedness gating, composite pairwise affinity formulations, two-stage graph coarsening Normalized Cuts algorithm, windowed quadrant segmentation, and empirical evaluation metrics.

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Citation

MLA

Malik, J., et al. “Contour and Texture Analysis for Image Segmentation”. International Journal of Computer Vision, vol. 43, no. 1, 2001, pp. 7–7, https://doi.org/10.1023/A:1011174803800.

APA

Malik, J., Belongie, S., Leung, T., & Shi, J. (2001). Contour and Texture Analysis for Image Segmentation. International Journal of Computer Vision, 43(1), 7–27. https://doi.org/10.1023/A:1011174803800

Chicago

Malik, J., S. Belongie, T. Leung, and J. Shi. 2001. “Contour and Texture Analysis for Image Segmentation”. International Journal of Computer Vision 43 (1): 7–27. https://doi.org/10.1023/A:1011174803800.

Harvard

Malik, J. et al. (2001) “Contour and Texture Analysis for Image Segmentation”, International Journal of Computer Vision, 43(1), pp. 7–27. Available at: https://doi.org/10.1023/A:1011174803800.

Vancouver

1. Malik J, Belongie S, Leung T, Shi J (2001) Contour and Texture Analysis for Image Segmentation. International Journal of Computer Vision 43:7–27

BibTeX

@article{Malik_2001, title={Contour and Texture Analysis for Image Segmentation}, volume={43}, ISSN={1573-1405}, url={http://dx.doi.org/10.1023/A:1011174803800}, DOI={10.1023/a:1011174803800}, number={1}, journal={International Journal of Computer Vision}, publisher={Springer Science and Business Media LLC}, author={Malik, Jitendra and Belongie, Serge and Leung, Thomas and Shi, Jianbo}, year={2001}, month=June, pages={7–27} }

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Contour and Texture Analysis for Image Segmentation

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Texton Generation and Filter Bank Architecture

Knowl 2 — Texturedness Gating Operator for Cue Combination

Knowl 3 — Gated Pairwise Affinity Metric Combining Contour and Texture

Knowl 4 — Adaptive Local Texture Scale Selection via Delaunay Triangulation

Knowl 5 — Two-Stage Spectral Graph Partitioning via Graph Coarsening

Knowl 6 — Windowed Segmentation Framework for Large Scale Images

Knowl 7 — Empirical Segmentation Performance and Computational Efficiency

References

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