We model the difference between two histograms as a temperature field and study the relationship between histogram similarity and a diffusion process, showing how diffusion handles deformation as well as quantization effects. As a result, the diffusion distance is derived as the sum of dissimilarities over scales. Being a cross-bin histogram distance, the diffusion distance is robust to deformation, lighting change and noise in histogram-based local descriptors. In addition, it enjoys linear computational complexity which significantly improves previously proposed cross-bin distances with quadratic complexity or higher.
Diffusion Distance for Histogram Comparison, (with K. Okada), CVPR'06.

We propose a fast algorithm, EMD-$L_1$, for computing the Earth Mover's Distance (EMD) between histograms. Compared to the original formulation, EMD-$L_1$ has a largely simplified structure and is formally equivalent to the original EMD with L_1 ground distance. Exploiting the L_1 metric structure, an efficient tree-based algorithm is designed to solve the EMD-$L_1$ computation. An empirical study shows that EMD-L1 has the time complexity of $O(N^2)$, which is much faster than previously reported algorithms with super-cubic complexities.
An Efficient Earth Mover's Distance Algorithm for Robust Histogram Comparison, (with K. Okada), PAMI'07.

We propose a novel framework to build descriptors of local intensity that are invariant to general deformation. In this framework, an image is embedded as a 2D surface in 3D space, with intensity weighted relative to distance in $x$-$y$. We show that as this weight increases, geodesic distances on the embedded surface are less affected by image deformations. In the limit, distances are deformation invariant. We use geodesic sampling to get neighborhood samples for interest points, then use a geodesic-intensity histogram (GIH) as a deformation invariant local descriptor.
Deformation Invariant Image Matching, (with D.W. Jacobs), ICCV05. ICCV Talk (4.5M).

We found that the inner-distance which is defined as the shortest path length in shapes is (invariant) insensitive to (ideal) articulations. We demonstrated that it can be used to build very discriminative descriptors for shapes with parts, especially with articulations. In the experiments on several widely tested dataset including the MPEG7 shape dataset and the Kimia dataset, our approach outperforms all other reported methods.
Shape Classification Using the Inner-Distance, (with D.W. Jacobs), PAMI'07. Articulated shape data

Use machine learning techniques, we designed methods for the specimen images processing, including frame removing and background elimination and leaf/stem labeling. The basic idea is to combine k-means and SVM on region-based features.

Currently we are doing further experiments on leaf-segmentation using graph models and tryiing to apply the statistical shape theory to capture the leaf deformations.

This part of work focuses on leaf image classification. We designed experiments on some leaf image databases, including Fourier descriptor, shape context, and inner-distance shape context. Beside of that, some early experiments for model based leaf detection from specimen image are conducted, where we combine the mean-shift and the generalized Hough transform. We use the statistical method to model the leaf shapes to allow deformations. A short report of the earlier work can be found at report at Smithsonian, 09/2003 (6M)

To show that the detection method is generic, we also tested the method with several medical images from Falzenswalb's paper.