You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Compact and discriminative visual codebooks are preferred in many visual recognition tasks. In the literature, a number of works have taken the approach of hierarchically merging visual words of an initial large-sized codebook, but implemented this approach with different merging criteria. In this work, we propose a single probabilistic framework to unify these merging criteria, by identifying two key factors: the function used to model class-conditional distribution and the method used to estimate the distribution parameters. More importantly, by adopting new distribution functions and or parameter estimation methods, our framework can readily produce a spectrum of novel merging criteria. Three of them are specifically focused in this work. In the first criterion, we adopt the multinomial distribution with Bayesian method; In the second criterion, we integrate Gaussian distribution with maximum likelihood parameter estimation. In the third criterion, which shows the best merging performance, we propose a max-margin-based parameter estimation method and apply it with multinomial distribution. Extensive experimental study is conducted to systematically analyse the performance of the above three criteria and compare them with existing ones. As demonstrated, the best criterion obtained in our framework achieves the overall best merging performance among the comparable merging criteria developed in the literature.

Cited Abstract(s):
[1]: In patch-based object recognition, using a compact visual codebook can boost computational efficiency and reduce memory cost. Nevertheless, compared with a large-sized codebook, it also risks the loss of discriminative power. Moreover, creating a compact visual codebook can be very time-consuming, especially when the number of initial visual words is large. In this paper, to minimize its loss of discriminative power, we propose an approach to build a compact visual codebook by maxi- mally preserving the separability of the object classes. Furthermore, a fast algorithm is designed to accomplish this task effortlessly, which can hierarchically merge 10,000 visual words down to 2 in ninety seconds. Experimental study shows that the compact visual codebook created in this way can achieve excellent classification performance even after a considerable reduction in size.
: In [1] , the scatter-matrix-based class separability, @math , is used to measure the goodness of @math as where @math and @math are the within-class scatter matrix and the total scatter matrix, respectively. @math denotes the trace of a matrix. They are computed with training histograms @math . At each level, the words @math and @math whose mergence minimizes @math are identified and merged To facilitate the subsequent analysis, we use the minimization of @math here. Because of the identity @math , it is equivalent to [1] which maximizes @math . .