Nina S. T. Hirata

Automatic Programming of Morphological Machines by PAC Learning

An important aspect of mathematical morphology is the description of complete lattice operators by a formal language, the Morphological Language (ML), whose vocabulary is composed of infimum, supremum, dilations, erosions, anti-dilations and anti-erosions. This language is complete (i.e., it can represent any complete lattice operator) and expressive (i.e., many useful operators can be represented as phrases with relatively few words). Since the sixties special machines, the Morphological Machines (MMachs), have been built to implement the ML restricted to the lattices of binary and gray-scale images. However, designing useful MMach programs is not an elementary task. Recently, much research effort has been addressed to automate the programming of MMachs. The goal of the different approaches for this problem is to find suitable knowledge representation formalisms to describe transformations over geometric structures and to translate them automatically into MMach programs by computational systems. We present here the central ideas of an approach based on the representation of transformations by collections of observed-ideal pairs of images and the estimation of suitable operators from these data. In this approach, the estimation of operators is based on statistical optimization or, equivalently, on a branch of Machine Learning Theory known as PAC Learning. These operators are generated as standard form morphological operators that may be simplified (i.e., transformed into equivalent morphological operators that use fewer vocabulary words) by syntactical transformations.

Fast QR Code Detection in Arbitrarily Acquired Images

The detection of QR codes, a type of 2D barcode, as described in the literature consists merely in the determination of the boundaries of the symbol region in images obtained with the specific intent of highlighting the symbol. However, many important applications such as those related with accessibility technologies or robotics, depends on first detecting the presence of a barcode in an environment. We employ Viola-Jones rapid object detection framework to address the problem of finding QR codes in arbitrarily acquired images. This framework provides an efficient way to focus the detection process in promising regions of the image and a very fast feature calculation approach for pattern classification. An extensive study of variations in the parameters of the framework for detecting finder patterns, present in three corners of every QR code, was carried out. Detection accuracy superior to 90%, with controlled number of false positives, is achieved. We also propose a post-processing algorithm that aggregates the results of the first step and decides if the detected finder patterns are part of QR code symbols. This two-step processing is done in real time.

A switching algorithm for design of optimal increasing binary filters over large windows

Abstract All known approaches for the design of increasing translation-invariant binary window filters involve combinatoric searches. This paper proposes a new switching algorithm having the advantage that the search is over a smaller set than other algorithms. Beginning with an estimate from image realizations of the optimal generic (nonincreasing) window function, the algorithm switches (exchanges) a set of observation vectors (templates) between the optimal functions kernel and the kernels complement. There are many such “switching sets” that provide a kernel defining an increasing filter. The optimal increasing filter is the one corresponding to the switching set that produces the minimal increase in error over the optimal generic filter. The core of the search problem is the inversion set of the optimal filter. The inversion set is composed of all vectors in the kernel lying beneath a nonkernel vector in the lattice of observation vectors and all nonkernel vectors lying above a kernel vector. The new algorithm, which is based on an error-related greedy property, recursively eliminates the inversion set until the optimal increasing filter is obtained. For purposes of computational efficiency, the actual implementation may be based on a relaxation of the original construction, so that the result may be based on a relaxation of the original construction, so that the result may be suboptimal. For the various models tested, the relaxed algorithm has proven to be optimal or very close to optimal. Besides its good estimation precision, the new algorithm has three noteworthy properties: first, it is applicable to relatively large windows; second, it operates directly on the input data via estimates of the determining conditional probabilities; and third, the degree of relaxation serves as an input parameter to the algorithm, so that computation time can be bounded for large windows and the algorithm can run to full optimality for small windows.

Multilevel Training of Binary Morphological Operators

The design of binary morphological operators that are translation-invariant and locally defined by a finite neighborhood window corresponds to the problem of designing Boolean functions. As in any supervised classification problem, morphological operators designed from training sample also suffer from overfitting. Large neighborhood tends to lead to performance degradation of the designed operator. This work proposes a multi-level design approach to deal with the issue of designing large neighborhood based operators. The main idea is inspired from stacked generalization (a multi-level classifier design approach) and consists in, at each training level, combining the outcomes of the previous level operators. The final operator is a multi-level operator that ultimately depends on a larger neighborhood than of the individual operators that have been combined. Experimental results show that two-level operators obtained by combining operators designed on subwindows of a large window consistently outperforms the single-level operators designed on the full window. They also show that iterating two-level operators is an effective multi-level approach to obtain better results.

An Exact Algorithm for Optimal MAE Stack Filter Design

We propose a new algorithm for optimal MAE stack filter design. It is based on three main ingredients. First, we show that the dual of the integer programming formulation of the filter design problem is a minimum cost network flow problem. Next, we present a decomposition principle that can be used to break this dual problem into smaller subproblems. Finally, we propose a specialization of the network Simplex algorithm based on column generation to solve these smaller subproblems. Using our method, we were able to efficiently solve instances of the filter problem with window size up to 25 pixels. To the best of our knowledge, this is the largest dimension for which this problem was ever solved exactly

Iterative design of morphological binary image operators

Iterating (composing) a sequence of window operators results in an operator defined over the window determined by the dilation of the component windows. Although a statistically designed iterative operator uses potentially all of the variables in the large dilated window, the design of each component operator requires design only over a much smaller component window, thereby resulting in a reduced estimation error. This means that designed iterative operators can perform better than designed estimates of fully optimal operators over the same effective window. While the optimal iterative and fully optimal operators may differ substantially in their logical structure, they may be probabilistically very close as operators on the random image processes under consideration. Thus, a precisely designed iterative operator can be closer to optimal than a less precisely designed unconstrained operator. We present three measures by which to compare iterative operators, with main interest focusing on the difference in their mean-absolute errors (MAEs), and discuss iterative design procedures and relationships between MAEs occurring from various procedures. A key aspect of design is the dependency on sample size. Increasing the number of iterations may in theory produce a better filter but, like using large windows, increasing the number of iterations increases the amount of data required for precise design. We pay particular attention to this issue. Using both restoration and recognition operators, we consider the best number of iterations and window size. We also consider the manner in which the training data should be split when designing the individual component operators. Iteration number, window size, and training method are all dependent on the filtering task, image characteristics, and amount of training data available.

Mathematical Symbol Hypothesis Recognition with Rejection Option

In the context of handwritten mathematical expressions recognition, a first step consist on grouping strokes (segmentation) to form symbol hypotheses: groups of strokes that might represent a symbol. Then, the symbol recognition step needs to cope with the identification of wrong segmented symbols (false hypotheses). However, previous works on symbol recognition consider only correctly segmented symbols. In this work, we focus on the problem of mathematical symbol recognition where false hypotheses need to be identified. We extract symbol hypotheses from complete handwritten mathematical expressions and train artificial neural networks to perform both symbol classification of true hypotheses and rejection of false hypotheses. We propose a new shape context-based symbol descriptor: fuzzy shape context. Evaluation is performed on a publicly available dataset that contains 101 symbol classes. Results show that the fuzzy shape context version outperforms the original shape context. Best recognition and false acceptance rates were obtained using a combination of shape contexts and online features: 86% and 17.5% respectively. As false rejection rate, we obtained 8.6% using only online features.

A Machine Learning Based Method for Staff Removal

Staff line removal is an important pre-processing step to convert content of music score images to machine readable formats. Many heuristic algorithms have been proposed for staff removal and recently a competition was organized in the 2013 ICDAR/GREC conference. Music score images are often subject to different deformations and variations, and existing algorithms do not work well for all cases. We investigate the application of a machine learning based method for the staff removal problem. The method consists in learning multiple image operators from training input-output pairs of images and then combining the results of these operators. Each operator is based on local information provided by a neighborhood window, which is usually manually chosen based on the content of the images. We propose a feature selection based approach for automatically defining the windows and also for combining the operators. The performance of the proposed method is superior to several existing methods and is comparable to the best method in the competition.

Automatic labeling of handwritten mathematical symbols via expression matching

Mathematical expression recognition is one of the challenging problems in the field of handwritten recognition. Public datasets are often used to evaluate and compare different computer solutions for recognition problems in several domains of applications. However, existing public datasets for handwritten mathematical expressions and symbols are still scarce both in number and in variety. Such scarcity makes large scale assessment of the existing techniques a difficult task. This paper proposes a novel approach, based on expression matching, for generating ground-truthed exemplars of expressions (and, therefore, of symbols). Matching is formulated as a graph matching problem in which symbols of input instances of a manually labeled model expression are matched to the symbols in the model. Pairwise matching cost considers both local and global features of the expression. Experimental results show achievement of high accuracy for several types of expressions, written by different users.

An Information Theory framework for two-stage binary image operator design

The design of translation invariant and locally defined binary image operators over large windows is made difficult by decreased statistical precision and increased training time. We present a complete framework for the application of stacked design, a recently proposed technique to create two-stage operators that circumvents that difficulty. We propose a novel algorithm, based on Information Theory, to find groups of pixels that should be used together to predict the output value. We employ this algorithm to automate the process of creating a set of first-level operators that are later combined in a global operator. We also propose a principled way to guide this combination, by using feature selection and model comparison. Experimental results show that the proposed framework leads to better results than single stage design.