(d) The time for training and testing the SVMs are comparable for both the descriptors.
Thus, on the whole, we observe that the proposal of the present Chapter takes lesser time for computation when compared to the one in Chapter 2.
3.8 Conclusion
We conclude this Chapter with an enumeration of the contributions:
(i) Proposal of descriptors derived from a set of dictionary atoms. The descriptors for each dictionary atom encode the error while using it alone for reconstruction.
(ii) Utilization of histogram based feature vectors extracted at a sub-stroke level, together with their corresponding sparse coefficients, for deriving the sparse coded descriptors.
(iii) Proposal of an entropy based analysis for the appropriate bin size to be selected for obtaining the features so as to ensure the discrimination between the writer descriptors.
4
Exploration of saliency information in the sparse framework
Contents
4.1 Introduction . . . 82 4.2 Schematic of the proposed framework . . . 84 4.3 Entropy based saliency computation . . . 85 4.4 Sum-pooling based saliency computation . . . 91 4.5 Modified Writer Descriptor . . . 93 4.6 Writer specific saliency value adaptation . . . 96 4.7 Experiments and discussion . . . 101 4.8 Conclusion . . . 107
4.1 Introduction
In this Chapter, we attempt to explore additional information from the sparse coding co- efficients that can be useful for writer identification. Recall from Section 3.5 that traditional sparse representation based classification strategies consider the accumulation of sparse coef- ficients over a set of dictionary atoms followed by a averaging process. The averaged value from each dictionary atom as such is used as a feature vector for classification. This strategy is termed as mean / average pooling. Likewise, another technique is that of max pooling where in the maximum of a set of sparse coefficients is computed for each dictionary atom in lieu of the average value. In this work, we propose to reformulate the above strategies by taking into regard prior knowledge that is obtained from the set of dictionary atoms.
The additional information, as we shall see, is related to quantifying in an average sense, the degree of importance of each of the dictionary atoms with regards to the dynamic charac- teristics of the enrolled writers. In this context, we define in this work, the term “saliency” 1 for an dictionary atom - the value of which is learnt from the sparse coefficients corresponding to the sub-strokes of the handwritten training data. In order to calculate its value, we propose two separate strategies as outlined below.
• In the first method, the saliency values for the over-complete set of dictionary atoms are obtained from computing entropy measures over histograms generated from the sparse coefficients. The number of histograms considered for this strategy correspond to the size of the dictionary.
• Our second technique for determining the saliency utilizes a single histogram, that is generated from sum pooling the sparse coefficients over all the feature descriptors of sub- strokes segmented from the training data. The calculation of its value, as we shall see, relies on an equation, that bears semblance to that of the inverse document frequency (idf) used in the area of document image retrieval.
1In this thesis on online writer identification, this term is not to be interpreted to that used by researchers of the image processing and computer vision community.
4.1 Introduction
During the identification of a test document, the saliency values (computed by one of the above two proposals) serve as a-priori information, that can be incorporated in the traditional frame- work of max or average pooling. This, in turn leads to a modified descriptor, that can be used for establishing the author of the document under question. To the best of our knowledge, the proposed saliency computation outlined in this Chapter is a first of its kind to be used in the sparse coding domain. Experiments performed with the proposed sparse classification strategy shows improved writer identification rates over the traditional schemes.
Further to the above, we also consider incorporating writer-specific adaptation of saliency values, that quantifies how important a dictionary atom is for a given writer. Our approach, as we shall see in this Chapter, employs the reconstruction error on the sub-stroke based feature vectors to derive a similarity score for each dictionary atom with regards to a writer using only his / her handwriting. The obtained scores across all the dictionary atoms are subsequently fused with their respective saliency values 2 to generate the adapted values for the purpose of identification. In particular, we formulate an ensemble of SVMs, wherein the descriptor to the SVM trained for a writer is based on the saliency values adapted for that writer. The final decision on the authorship is proposed as the maximum of the prediction score obtained from the SVMs.
In the subsequent Sections, we present details of each of the contributions made in this Chapter. To begin with, we provide a block schematic of our proposed framework, that em- ploys the saliency information of the dictionary atoms in Section 4.2. In order to compute these values, we consider two new strategies - the details of which are described in Sections 4.3 and 4.4 respectively. Subsequent to obtaining the saliency of dictionary atoms, we discuss their incorporation into the traditional sparse framework in Section 4.5, that leads in a modified writer descriptor. As an extended idea in Section 4.6, we present our approach of determining writer specific adapted saliency values and their utilization in writer identification. Last but not the least, several experiments have been outlined in Section 4.7 to establish the various
2These values correspond to those obtained without adaptation and quantify the importance of the atoms with regards to the average dynamic characteristics of the enrolled writers.
aspects of our contributions to writer identification.