Abstract— In this paper we present an image size invariant method for quick detection of dissimilar binary images. The method is based on a Probabilistic Matching Model (PMM) for binary image matching. Using the model, the probability of matching dissimilar image pairs can be predicted, as a function of the number of points mapped between two images and the amount of similarity between them. The model tells us that by matching few points between two images, we can determine dissimilar images with high confidence. For example, if images are distinct-dissimilar, i.e., completely different, only 8 points need to be mapped to arrive at a 90% successful detection rate, 11 points need to be mapped for a 99% confidence detection rate and only 15 points need to be mapped for a 99.9% confidence detection rate. If the images are not distinct- dissimilar and the images have some similarity between them, then more points need to be matched; depending on the amount of similarity between the images. The model is image size invariant and hence images of any sizes will produce the same high confidence levels with only a limited number of points. As a result, this method does not suffer from the image size handicap that current methods suffer from. We report on tests conducted on real images of different sizes to show the validity of our model. Index Terms— binary images, image mapping, image matching and probabilistic model. I. INTRODUCTION MAGE matching rises frequently in the field of image analysis under many topics such as, image registration, template matching, image retrieval, image classification, etc. These methods are either feature-based methods that rely on some method of extracting image features and then matching the extracted features, or area-based methods (also referred to as direct or intensity methods) that are based on comparing image intensity values directly without any feature extraction. When dealing with binary images, and due to the fact that they have only two intensity values resulting in a limited amount of scene detail, feature-based methods become difficult to employ, and area-based methods become the method of choice. Binary image matching is usually accomplished by calculating the cross-correlation between the images [1] or simply by subtracting the two images [2]. These methods, as well as the majority –if not all– of area-based methods require some type of similarity operation to be applied to the whole image. Hence, these methods are image size dependent which implies that as image size increases, more processing time is required. With 20 Mega-pixel images common and 50 Mega-pixel images becoming easily Manuscript received December 8, 2014; revised February 1, 2015. Adnan A. Mustafa is with the Department of Mechanical Engineering, Kuwait University, P. O. Box 5969-Safat, Kuwait 13060 (phone: (+965) 24987117, Fax:(+965) 24847131; E-mail: adnan.mustafa@ku.edu.kw). producible with recently introduced inexpensive digital cameras or even mobile phones, current matching methods can become quite slow processing such large images, even with today’s fast computers. In this paper we present an image size invariant method for quick detection of dissimilar binary images. The method is based on a Probabilistic Matching Model (PMM) for binary image matching [3]. Using the model, the probability of matching dissimilar image pairs can be predicted, as a function of the number of points mapped between two images and the amount of similarity between them. The model tells us that by matching few points between two images, we can determine dissimilar images with high confidence. For example, if images are distinct-dissimilar, i.e., completely different, only 8 points need to be mapped to arrive at a 90% successful detection rate, 11 points need to be mapped for a 99% confidence detection rate and only 15 points need to be mapped for a 99.9% confidence detection rate. If the images are not distinct-dissimilar and the images have some similarity between them, then more points need to be matched; depending on the amount of similarity between the images. The model is image size invariant and hence images of any sizes will produce the same high confidence levels with only a limited number of points. As a result, this method does not suffer from the image size handicap that current methods suffer from. We report on tests conducted on real images of different sizes to show the validity of our model. This paper is organized as follows: section II points out related literature, section III reviews the binary image similarity measure used as a reference in our work, section IV presents binary image mappings and how they can simplify binary matching, section V presents the main theme of this paper and presents the theory of the probabilistic matching model, section VI presents results of tests conducted on real images and their agreement with the theoretical model and section VII finally concludes our findings and discusses where our future research is directed. II. RELATED LITERATURE Cross-correlation is the most widely used method for image matching. Many techniques have attempted to improve using cross-correlation; Lebrl [4] counted the change in mismatched pixels as the template sweeps the image. Lewis [5] used pre-computed tables containing the integral of the image and the image 2 search window. Mattoccia et al. [6] presented a zero-mean normalized cross- correlation to reduce the computational cost. Other area-based methods have also been developed based on a variety of principles. For example, Mustafa et al. [7] matched images by minimizing the image intensity combinations with excellent results. However, the method is An Image Size Invariant Method for Quick Detection of Dissimilar Binary Images Adnan A. Y. Mustafa, Member, IAENG I Proceedings of the International MultiConference of Engineers and Computer Scientists 2015 Vol I, IMECS 2015, March 18 - 20, 2015, Hong Kong ISBN: 978-988-19253-2-9 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) IMECS 2015