AdaContour: Adaptive Contour Descriptor with Hierarchical Representation

TL;DR

AdaContour tackles the limitation of single-global angle-based contour descriptors on non-starconvex shapes by introducing hierarchical encoding to produce multiple local contours and a shared low-rank subspace learned via robust subspace recovery. The method reconstructs object boundaries by projecting local contours onto a universal basis and reassembling them, enabling accurate representation with few coefficients. Empirical results show clear advantages over single-contour baselines across multiple datasets and tasks, including improved IOU and competitive instance-segmentation performance when integrated with YOLOv3, while maintaining efficiency through early stopping and basis-sharing. The approach offers a scalable, robust descriptor for complex shapes with potential extensions to end-to-end segmentation, shape deformation, and generative modeling.

Abstract

Existing angle-based contour descriptors suffer from lossy representation for non-starconvex shapes. By and large, this is the result of the shape being registered with a single global inner center and a set of radii corresponding to a polar coordinate parameterization. In this paper, we propose AdaContour, an adaptive contour descriptor that uses multiple local representations to desirably characterize complex shapes. After hierarchically encoding object shapes in a training set and constructing a contour matrix of all subdivided regions, we compute a robust low-rank robust subspace and approximate each local contour by linearly combining the shared basis vectors to represent an object. Experiments show that AdaContour is able to represent shapes more accurately and robustly than other descriptors while retaining effectiveness. We validate AdaContour by integrating it into off-the-shelf detectors to enable instance segmentation which demonstrates faithful performance. The code is available at https://github.com/tding1/AdaContour.

Figures (9)

• Figure 1: Two challenging examples in the SBD dataset hariharan2011semantic. Existing dominant contour descriptors that use a single global representation fail to capture subtle regions of the shapes, such as the beak of the bird and the legs of the table, for each choice of $M$ that controls the expressive ability. In sharp contrast, our approach with multiple local representations yields high quality results.
• Figure 2: Illustration of hierarchical encoding. (a) Image with ground-truth object boundaries. (b) Starconvex contours generated by park2022eigencontours. (c)-(e): Adaptive contours generated by our hierarchical encoding procedure, which recursively subdivides the initial possibly non-convex shape and terminates when a sufficiently regular area is identified or maximum depth is reached, then each subdivision is encoded by a local contour. In the example, the object boundary of the lady is starconvex, rendering a single global contour sufficient for its representation. The man's boundary is more complex, and a single contour cannot faithfully represent the face, hand and chin. Hierarchical encoding is effective in resolving the issue by subdividing the shape adaptively and conquering each of them locally. By setting the depth to 1 and utilizing only 2 centers, the representation of the face and hand of the man is more precise. The hand shape becomes more distinctive at depth 2, and the depiction of the chin is rendered correctly at depth 5. Note that as the hierarchical depth increases, newly introduced local contours automatically converge around the challenging areas.
• Figure 3: Reorganization of disconnected components. Disconnected components can sometimes result from splitting the shape based on the direction of the least data variance. We handle the issue by retaining the component with the largest area and returning the other parts to the remainder of the partition.
• Figure 4: Visualization of the five basis vectors in $\bm U^\star$ with $M=5$. Top to bottom: we increase depth $D$ for encoding all instances in the COCO2017 dataset lin2014microsoft.
• Figure 5: Effective rank of the contour matrix constructed with different hierarchical depths $D$. As $D$ increases, the effective rank of the contour matrix decreases, suggesting more correlation among the contours.

Theorems & Definitions (1)

• Proposition 1