image processing

final project


I. Intro

                I initially tried toquantify each image in terms of vehicles that were present.   After viewing the magnitude of the FFTs,two lines were present within the spectrum. After talking with Dr. Sakaar, he mentioned that these lines maycorrespond to the particular direction of the frequency.  So, I also looked at the angle of view ofeach image with this information as well.


Ilooked at a total of five images.  Eachimage had a varying amount of information or vehicles.  I arranged the images from left to right,top to bottom with the top left image of each sequence corresponding to theleast amount of vehicles.  Eachsuccessive image has an increased amount of cars.  The printouts do not give great details to the images so I willhave a copy of this report, Microsoft Word format, at my web site, 


Ifirst would like to talk about the angle of view in each image.  Secondly I would like to mention theapproach I took in trying to quantify each image.

II. Original  Images

            These are the five original imagesin which Dr. Sakaar asked me to investigate.



















































III. Report

With both areas of interest, the angle of view andquantity, I took the FFT with the low frequencies centered in the image.

A.    Angle of View























































I could right away work with the magnitude of eachimage from the FFTs above to notice at what angle each image was takenfrom.  By taking the angles of the sameFFTs one can obtain a good approximation of the viewing angle of the originalimages.  Of course this data issubjected to the design of the parking lot. The angles that differ from 90 degrees are viewed from an angle that isleft of right of each picture and with some distance between the parking lotand the camera.  If one were directly infront or directly looking at the side of the lot, the angles would not deviatetoo much from 90 degrees.  Images oneand two both show some degree of orientation and the FFT’s magnitude doesdisplay an angle proportional to the view of the camera.  The magnitudes are particularly strong sincethe intensities of the parking lot and of its immediate surroundings varygreatly.  The other three images displayless of a tilt and their FFTs corroborate that notion as well. 



B. Quantity


            I initially looked at the magnitudeof the FFT and with Dr. Sakaar’ advice took vary areas of the frequencies inthe spectrum.  I accomplished thisthrough a band pass filter.  I thenplotted the results as seen from below. 



I first normalized the frequencies of the FFTs toone.  Then I applied a log10 scaling tohelp visualize the FFT results.  Next, Iapplied a band pass filter with an inner radius of one pixel.  I choose a radius of one since theinformation of the center of the FFT was not needed since the value is alreadyknown to be one.  The omission of thecenter pixel also kept the graph at more favorable scale along the Y-axis.  I took the Root Mean Square of all theintensities within the band pass filter and graphed the results versus thevarying outer ring of the filter. Please see figures below.
























































I had expected the magnitude of frequency wouldbecome lower as the vehicles increased in each image.  The first, third, fourth, and fifth images seemed to agree withmy expectations.  However, I would havethought the Y-axis or the  lowfrequencies would have deviated more than what was shown.  Also, surprisingly, the second imagecontains more low frequencies, than the first image.  Both of the above factors maybe explainable.  The band pass filter took into account allof the varying directions of the frequencies. The FFTs shows approximately only two directions.  These two main directions do correspond tothe orientation of the vehicles.  If Ihad focused my attention on the magnitude of the frequencies in the two visiblelines, then I could perhaps arrive at a more satisfactory conclusion.  By concentrating on the two lines I couldomit the other unnecessary frequencies.