Thresholded Convolutions Operations

Abstract

Thresholded convolution operations occur frequently in picture-processing algorithms and in special pict ure-processing hardware, such as image storage tubes. A number of theorems revealing some of the effects of combining the thresholding operation with tlle convolution operation are derived. In particular it is shown that a discrete convolution operation takes binary-valued functions into binary-valued functions if and only if it is a translation or identically zero. It is also shown that no thresholded nonzero convolution (i.e. a nonzero convolution followed by a thresholding) is equivalent to an unthresholded discrete convolution.KEY WORDS AND PHRASES: thresholded operations, convolution, discrete linear operations, correlation, t)icture-proccssing, image storage lube, edge enhancement, image-processing, optical-processing, matched tilter, pattern recognition CR CATEGORI.ES: 3.63, 3.69, 5.39, 6.22 Inh'oductionThresholded convolution operations, of which simple threshohling is a special case, occur frequently in picture-processing by machine. For example, converting a continuous-tone picture into a set of black blobs on a white background, with the black blobs approximating a connected range of the gray scale, often requires a combination of convolutions and thresholding operations [1]. The outlining and smoothing of the edges of the blobs are also usually implemented by sequences of thrcsholded convolutions [2,3]. An electronic picture-processing device, called the "image storage tube," is particularly suited to implementing thresholded convolutions [4][5][6].In the present paper we derive a number of theorems that reveal some of the significance of the thresholding operation. In particular we show that no thresholded operation (i.e. an operation followed by a thresholding) is equivalent to a convolution.The work here suggests a new direction of research into picture-processing by parallel operations. Nolation and Basic Definitions

Pakolaisten kriminalisointi

“…Poliisi ja turvallisuusviranomaiset voivat valita tehokkaimman keinon -olipa se sitten rikosoikeudellinen tai hallinnollinenidentifioidakseen epäilyttävän muukalaisen ja arvioidakseen hänen oikeuttaan olla maassa. 6 Tässä on rakennuspalikat uudelle oikeudelliselle rinnakkaisjärjestelmälle, jossa "maahanmuuttolainsäädäntö ja rikosoikeusjärjestelmä erottuvat toisistaan vain nimellisesti". 7 Maahanmuuton kontrollointi toteutetaan rikosoikeudellisesti hyödyntäen sen kriminalisointisäännöksiä ja niiden oikeuttamaa rangaistus-ja väkivaltakoneistoa.…”