An Algebraic Approach to Hough Transforms

The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from problems of detection of special shapes in medical and astronomical images. The classical Hough transform has been used mainly to detect simple curves such as lines and circles. We generalize this notion using reduced Groebner bases of flat families of affine schemes. To this end we introduce and develop the theory of Hough regularity. The theory is highly effective and we give some examples computed with CoCoA

Corrigendum for "Almost vanishing polynomials and an application to the Hough transform"

In this note we correct a technical error occurred in [M. Torrente and M.C. Beltrametti, "Almost vanishing polynomials and an application to the Hough transform", J. Algebra Appl. 13(8), (2014)]. This affects the bounds given in that paper, even though the structure and the logic of all proofs remain fully unchanged.Comment: 30 page

A Detailed Investigation into Low-Level Feature Detection in Spectrogram Images

Being the first stage of analysis within an image, low-level feature detection is a crucial step in the image analysis process and, as such, deserves suitable attention. This paper presents a systematic investigation into low-level feature detection in spectrogram images. The result of which is the identification of frequency tracks. Analysis of the literature identifies different strategies for accomplishing low-level feature detection. Nevertheless, the advantages and disadvantages of each are not explicitly investigated. Three model-based detection strategies are outlined, each extracting an increasing amount of information from the spectrogram, and, through ROC analysis, it is shown that at increasing levels of extraction the detection rates increase. Nevertheless, further investigation suggests that model-based detection has a limitation—it is not computationally feasible to fully evaluate the model of even a simple sinusoidal track. Therefore, alternative approaches, such as dimensionality reduction, are investigated to reduce the complex search space. It is shown that, if carefully selected, these techniques can approach the detection rates of model-based strategies that perform the same level of information extraction. The implementations used to derive the results presented within this paper are available online from http://stdetect.googlecode.com

Identification of Musical Instruments by means of the Hough-Transformation

In order to distinguish between the sounds of different musical instruments, certain instrument-specific sound features have to be extracted from the time series representing a given recorded sound. The Hough Transform is a pattern recognition procedure that is usually applied to detect specific curves or shapes in digital pictures (Shapiro, 1978). Due to some similarity between pattern recognition and statistical curve fitting problems, it may as well be applied to sound data (as a special case of time series data). The transformation is parameterized to detect sinusoidal curve sections in a digitized sound, the motivation being that certain sounds might be identified by certain oscillation patterns. The returned (transformed) data is the timepoints and amplitudes of detected sinusoids, so the result of the transformation is another ?condensed? time series. This specific Hough Transform is then applied to sounds played by different musical instruments. The generated data is investigated for features that are specific for the musical instrument that played the sound. Several classification methods are tried out to distinguish between the instruments and it turns out that RDA (a hybrid method combining LDA and QDA) (Friedman, 1989) performs best. The resulting error rate is better than those achieved by humans (Bruderer, 2003). --

Kannada Character Recognition System A Review

Intensive research has been done on optical character recognition ocr and a large number of articles have been published on this topic during the last few decades. Many commercial OCR systems are now available in the market, but most of these systems work for Roman, Chinese, Japanese and Arabic characters. There are no sufficient number of works on Indian language character recognition especially Kannada script among 12 major scripts in India. This paper presents a review of existing work on printed Kannada script and their results. The characteristics of Kannada script and Kannada Character Recognition System kcr are discussed in detail. Finally fusion at the classifier level is proposed to increase the recognition accuracy.Comment: 12 pages, 8 figure