Moment-preserving curve detection

A method is described for deriving, from digitiied imager.objective measures that correlate strongly with simple perceptual judge-ments on the same images. Each measure is the normalized variance of animage obtained by convolving the original image with a specific localoperator. This operator is designed to optimize the correlation between theparticular percept and the objective measure, subject to certain consbaint~. I. TEXTURALFEATURESThe analysis and characterization of visual textures is animportant requirement for both human and machine vision.Mathematical approaches have been developed for the purposesof feature extraction, pattern recognition, and scene segmenta-tion, as summarized in the surveys of Haralick [l]and Van Goo1et al. [2]. Machine discrimination of textures is an area ofconsiderable interest, requiring measurement of specific featuresrather than a knowledge of the underlying structure and synthesisof the texture. It would be of value if measures on digital imagesof textures could be found that correlated with human perfor-mance in discriminating these textures.In a significant experiment, Tamura el a/ . [3] attempted torelate objective measures of digitized textures to psychophysicaljudgements of the same textures on the basis of defined percep-tual criteria. They implemented different computational proce-dures for each of six scales, and obtained rank correlations in therange 0.65 to 0.90 between the psychological and objective mea-sures. In this paper, we investigate further the problem of findingmeasures on the digitized image that correlate highly with humanperception of texture.The results from our experiments suggest that the optimizationofa local operator offers the prospect of a general technique forthe determination of objective measures. There is an importantdifference between our approach and that of Tamura et a / . Theyaimed at measuring the correspondence between computationaldefinitions of textural features and psychophysical assessments.We have decided to use a general operator and adjust its parame-ters so as to optimize the correlation between objective measuresand psychophysical assessments. The psychological assessment ofthe textures used by Tamura et al. required a judgement basedon a verbally defined textural feature.We investigated three perceptual scales similar to those used in[3]. Subjects were asked to separately allocate imagesof texturesalong each of three psychological scales. These were line-likeversus bloblike nondirectional versus directional (where monodi-rectionality was ranked above bidirectionality), and randomversus regular. 11. OBJECTIVE MEASURES OF TEXTURAL FEATURESIn developing a mathematical approach to the problem oftexture characterization, we will describe the texture in statisticalrather than structural terms [l], [2]. The texture field is analysedby computing the statistics of the local properties after filteringwitha convolution mask [4], [5].In the past, these operators haveinspired models for edge detection because of their similarities tothe feature extractors believed to exist in the human visualsystem, as described, for example, by Marr161. Manuscript received Feb. 21. 1987: revised Nov. 3, 19x7The authors are with the Australian Department of Defence. Material, IEEE Log Number 8718873.Research Laboratories, P.O. Box 50. Ascot Vale. Victoria 3032. Aii,tralla 0018-9472/88/0100-0158$01.00 01988 IEEE