TWI285544B - System of iris imaging of pulse lighting and illuminant control - Google Patents

Abstract

A system of iris imaging of pulse lighting and illuminant control comprises an imaging device, a pulse lighting system controlled by illuminant controlling circuit and an analysis device. The imaging device takes primary and secondary pictures of an object by trapezoid pulse lighting cooperating with pulse lighting device at primary and secondary reserved times. The analysis device forms an intact iris image in linear combination from two iris images which extract from primary and secondary pictures after erasing primary and secondary abandoned areas lying to upper and lower positions of said primary and secondary pictures. Accordingly, the advantages of wider imaging range, more intact picture, safe lighting system, and easily recording images are presented.

Description

1285544 IX. Description of the Invention: [Technical Field] The present invention relates to an iris image capturing and light source control system, and more particularly to an iris image capturing and light source control system with pulsed light, which has a more image capturing range. Wide, more complete image, safe to play, light design and easy to record images and other benefits. [Prior Art]

The light source is the basic requirement for the integration and installation of the vision system. A well-designed light source system can reduce the complexity of image processing, greatly shorten the overall processing time, increase efficiency and increase A signal/noise ratio (S NR ) of an electrical coupling device (CCD) of an image capture system. If you ignore the techniques and precautions of the light source design, you must spend a lot of image correction time, you can get clear images that can be identified and analyzed, and reduce the chance of misjudgment. ^ The shape of an eyeball is arc-shaped, so when lighting, as long as the design of the position of the light source is not noticed, the light of the light source will be directly reflected into the CCD by means of mirror reflection, and a high brightness will be presented in the CCD. Reflective point, and this reflective point will make the detailed structure of the eyeball image unclear. The conventional iris image capturing device generally has two kinds of lighting methods, one is a single light source commonly used in the market, and the lighting position is fixed. Second, the use of a ring-type light source to illuminate the light source in the pupil. However, the following two methods of light-cutting have the following defects: [1] The image is incomplete. The single light source is lighted in the way that the light-emitting position 6 1285544 is fixed, leaving a reflective point on the iris. The area with the reflective point must be shaved during the detection, thus reducing the amount of information detected.

[2] The image capture range is limited. The ring type lighting method can concentrate the light source in the pupil, so that the iris area of the image to be taken has no reflection point, but when the subject is shooting the eyeball image, the posture will cause the up, down, left and right positions. The offset makes the ring light not concentrate in the pupil. Therefore, the face of the subject needs to be confined to a specific position, and the distance and the distance should be fixed, so that the image can be smoothly taken. If it is not in accordance with its requirements, it is easy to cause a reflective point on the iris, and the image capturing range is limited and there is no flexibility. Therefore, it is necessary to develop new products to solve the above drawbacks. SUMMARY OF THE INVENTION A primary object of the present invention is to provide a pulsed iris imaging and light source control system that has the advantage of a wider imaging range. A secondary object of the present invention is to provide a pulsed laser iris/image and light source control system that has the advantage of more complete image acquisition. It is still another object of the present invention to provide a pulsed iris imaging and light source control system having a safe lighting design. Still another object of the present invention is to provide a pulsed iris imaging and light source control system that achieves the goal of capturing images for easy recording. The invention provides a pulse-lighting iris image capturing and light source control system, which comprises an image capturing device, a light source control circuit, a pulse lighting system and an analyzing device, wherein: the image capturing device is in a first A predetermined time and a second predetermined time are matched with the lighting of the pulse lighting system, and a first image 7 1285544 image and a second image are captured on an object to be tested, and the first image and the second image are A first upper discarding zone and a second lower discarding zone are respectively generated; the light source control circuit controls the pulse lighting system to light the first predetermined time and the second predetermined time; the pulse and lighting The system performs trapezoidal pulse illumination on the object to be tested, and causes the first and second images to respectively generate a first reflection point and a second reflection point, wherein the first reflection point and the second reflection point are respectively Located on the first upper discarding zone and the second lower discarding zone;

The analyzing device takes out the iris regions of the first and second images respectively captured by the first predetermined time and the second predetermined time, and respectively separates the upper and lower areas of the first and second images 5 The second lower discarding area is shaved, and then the two iris images after shaving the first upper discarding area and the second lower discarding area are combined by linear combination to completely detect the complete image of the iris. The above objects and advantages of the present invention will be readily understood from the following detailed description of the embodiments of the invention. The present invention will be described in detail below with reference to the following embodiments: [Embodiment] In the optical arrangement of the image capturing system, most of the lighting systems use continuous light. For eye safety, a short pulse light can be used when measuring the eye. Come as an illumination source. Due to the multiple reflections of the object, the background light field of the image is taken. (ambient light or background light), for example: [1] diffuse reflection: refers to the light field reflected by the surface of the non-smooth object, without 'Smooth object surface in the background light field, the reflected light 8 1285544 field brightness can be written as follows: I = kdIa in it, t is the coefficient of reflection or reflectivity, the value is A real number from 0 to 1, when this value is close to 1, the case is called high reflectivity. Usually this light field is a scattered light. [2] Specular reflection: refers to the light field reflected by the surface of a smooth object.

The position of the eye's line of sight is calculated by the relationship between the direction of the incident light and the normal direction of the surface of the object. It is necessary to trace the interaction between the direction of the incident light and the normal direction of the surface of the object; for example, the calculation of the diffused light field is usually based on the Lanbert On the basis of the Lambert's cosine law, that is, between the direction of the incident light and the normal direction of the surface of the object, it can be expressed as follows:

cosO = N · L where N is the basic vector along the normal to the surface of the object. L is the basic vector along the incident 4 direction. Θ is the angle between the incident light and the normal direction of the surface of the object. After calculating the safety pulsed light data for the eye with reference to the foregoing data, a detection system platform is designed. Referring to the first and second figures, the present invention is a pulsed iris imaging and light source control system. The image capturing device 10 includes an image capturing device 1 , a light source control circuit 20 , a pulse lighting system 30 , and an analyzing device 40 . The image capturing device 10 is electrically connected by a universal flow channel 92 (referred to as a USB interface). a computer 91, the computer 91 is electrically connected to the light source control circuit 20 and the analysis device 40, wherein: 9

1285544 The image capturing device 10 is configured to have at least one image capturing lens 1 〇1, the image capturing lens time T1 and a second predetermined time T2, for a substantially one object to be tested 5 (assuming Shooting a second image 12 for an eye (see the ninth figure), the first shadow 12 is respectively generated with a first upper discarding area PU P 2 1, and in order to avoid the light source, the image is taken S is surrounded by a peripheral mask 13, the mask 13 is substantially continuous and the outside of the pulse lighting system 30; the light source control circuit 20 (shown in the third figure) is a series of transmission interface 21, Implementing RS - 2 3 2 serial transmission of the face, and closing the pulse (ie 1, 0) signal, and then controlling the pulse lighting system - a voltage level conversion element 2 2, is an A and a fourth B The figure is electrically connected to the string price shown in Figure 5) and is used to convert the serial transmission interface warning position (for example, from -12V to 12V to 0V~5V quasi-optical coupling element 23 (such as Figure 6) The optocoupler, which acts as a light signal, completely avoids the serial transmission of the face 2 1 suffered from reverse current breaking and an adjustable The regulated power supply circuit 24 (as in the seventh preferred embodiment, includes at least two transformers having an electro-crystalline voltage source of 12 V, and a variable resistor is provided to cause the pulse-lighting system 30 to emit moderate brightness. , the image capturing device 100.10 1 is located at a first predetermined position in the image capturing path L, the first image 1 1 and a .1 1 and the second image and a second lower abandonment area. 1 is taken in the image capturing lens 101, and includes at least: an L system 30 on a personal computer, a transmission, and a 30 flash; a MAX232IC (such as a fourth P input face 2 1 (eg, ^ 2 1) The voltage signal level); for example, a PC'8 1 7 blocking current signal, avoiding [; Ϊ), in the body of the invention, and adjusting the voltage by the input power. The light source control circuit is complete 10 1285544 line Referring to FIG. 8 , the pulse light-emitting system 30 includes at least two white light-emitting diodes (LEDs), and is respectively disposed on the image capturing device 101 of the image capturing device 10 . Below, the LED is controlled by the light source control # circuit 20 to turn on and off, with two white LEDs to light, The first and second reflection points 111 and a second reflection point 121 (as shown in FIG. 9) are generated on the first and second images 11 and 12, and the first and second reflection points 1 1 1 and 1 2 are generated. 1 is located in the first upper discarding zone P11 and the second lower discarding zone P21;

The analysis device 40 extracts the iris regions of the first image 1 1 and the second image 12 captured by the first predetermined time T1 and the second predetermined time T2 by the technique of image segmentation, and after the iris region is taken out, Each of the first and second images 11 and 12, the first upper discarding area P11 and the second lower discarding area P21 are shaved (as shown in the ninth and tenth figures), and then linearly inserted. In a manner, the two iris images of the first upper discarding zone P 1 1 and the second lower discarding zone P 2 1 are respectively shaved, so that a complete image of the iris can be completely detected. Iris image capture and light source control 'system. Please refer to the ninth, tenth and eleventh figures, which is the implementation of the pulse lighting system 30 of the system. Two white LEDs are placed on the upper and lower sides of the image taking lens 101 (as shown in the second figure). At the first predetermined time T1, the upper LED is lighted, and the first image 1 of the subject's eye is photographed. At the second predetermined time T2, the lower LEI is illuminated and the subject is photographed. The second image 12 of the eye. That is, within the brightness value of a point coordinate, the first and second images 1 1 and 1 2 are respectively taken at intervals of about 1 〇 milliseconds, that is, 11 1285544 is kept within the eye safety range.

In such a lighting and photography process, the eye image of the subject is transmitted to the analyzing device 40 through a digital camera, and the number of images to be taken and the number of seconds to be taken can be set (approximately one second is ingestible) 40 images, and can indicate the time and signal (trigger time) and lighting mode of each image, and increase the angle range of the image capturing posture of the subject, even if the subject's eye surface For the upper, lower, left and right offset of the image capturing lens 1 〇1, the light source of the LED still falls on the iris and the bottom of the subject, and is divided into the octagonal region of the TCM point of view. Thus, in the first image A first upper exclusion zone P 1 1 , a first lower security zone, a retention zone P 1 2 and a plurality of first merge zone P 1 3 are formed on the first image, and a second image is formed on the second image 12 a lower discarding zone P2 1 , a second upper retaining zone P22 and a plurality of second merged zones P23. The first image 1 1 taken at the first predetermined time T1 is in the first upper discarding zone P11 (about 67.5 degrees in the angle) Producing a first reflection point 1'1 1 to 112.5 degrees) The second image 12 captured by the predetermined time T2 generates a second reflection point 121 in the second lower discarding area P21 (about an angle of 247.5 degrees to 292.5 degrees). The first predetermined time is obtained by image segmentation. The iris regions of the first and second images 11 and 12 taken by T1 and the second predetermined time T2 are respectively taken out, and the first lower reserved area P12 of the first image 1 and the second upper reserved area P22 of the second image 12 are retained. , discarding the first image 1 1 and discarding the second PI 1 and the second lower disc area P21 of the second image 12, and then combining the first and second images 1 1 and 1 2 with the first and second merged areas P 1 3 Linearly combined with P2 3 12 1285544. Linear merging means that when the first and second images 11 are close to the upper half of the 1 2, the weight of the upper half is relatively large, and when the lower half is close, the weight of the lower half is Larger, linear interpolation is used to obtain the combined results.

That is, the first uppering < abandonment area PI 1 and the second lower discarding area P 2 1 having the reflective points 1 1 1 and 121 are respectively shaved, and the first and second are shaved by interpolation. Since the first and second images 11 and 12 after the reflection points 111 and 121 are combined, since there is no reflection point on the synthesized complete image 60, it is not necessary to shave any area, and the complete detection can be achieved. In order to ensure the effect of the imaged light field on the eye, the first predetermined time T 1 is approximately the middle period when the upper LED pulse light appears brightest and the brightness is reduced. At this time, the image capturing lens 1 1 is taken first. Image 1 1. The second predetermined time T2 is about after the appearance of the upper LED pulse light, and the brightness of the lower LED pulse is the same as the upper LED pulse light, and the eye size of the subject is about the same as the first image 1 1 . The second image 12 〇 such double-pulse light and the first upper discarding zone P 1 1 and the second lower discarding zone P 2 1 corresponding to the eye of the subject are approximately trapezoidal, and a better complete image of the iris can be obtained. 0, complete our iris detection device. As long as the double pulsed light and the first upper discarding zone P11 and the second lower discarding zone P2 1 corresponding to the eyes of the subject are approximately trapezoidal, even if the two white L· ED of the pulse lighting system 30 are changed. Lighting the left and right sides of the eye is also an equivalent replacement for the present invention. The invention adopts a white light LED as a light source for pulse illuminating, so it is necessary to understand the cursor related to the body (or eye) damage of the human 13 1285544. The generally strict 'light damage standard' is based on the safety limits of medical laser systems. Due to the high concentration of laser light, high density optical power density is the most harmful to the human body. Therefore, the safety consideration of the optical power of white light according to the present invention is based on the safety standard of medical laser to derive white LED. Safety restrictions on the eye to find the appropriate upper limit of the amount of light. The safety classification of the medical laser safety standard Z-1 3 6 · 1 is as follows: First stage The laser output power cannot be greater than the maximum allowable illumination power of the eye.

The second stage visible light laser output power does not exceed lmW. The third stage A laser beam output power is above 5mW. The third stage B laser beam output power is between 0.5mW and 0.5W.

The fourth stage laser beam output power is greater than 0.5W. The first level of safety classification is that the eyes can be directly observed, and no damage will be caused to the eyes. The present invention directly illuminates the white LED on the surface of the eye, but limits the power of the white light L E D . The safety limit of the white LED light power to the eye is derived by the above-mentioned safety limit of the first-order laser light of Z - 1 3 6.1, which does not cause damage to the eyes. The limit value of the maximum permissible exposure power (MPE) of the eye, as shown in Fig. 12, where ··· when the wavelength λ =400 ～550 nm, C5=l; when the wavelength λ =5 5 0 ～700 nm When Q = 10 [° ° 15 Bu 55 °)]; When the wavelength enters =400~5 5 0,11111, Tl = 10; When the wavelength λ = 5 5 0 ~700nm, ΤΙ = 10xl0_(A- 550)]; 14 1285544

Iks = 16.7 minutes, 500s = 8.3 minutes and related to the Correction Factor A and wavelength relationship, as shown in Figure 13, where: when the wavelength λ = 40 0~700nm, the heart = 1; when the wavelength λ = In the range of 700nm to 1 050nm, (^=10_2(A-7°°); (1) When the wavelength is λ = 1050nm~1400nm, CA= 5 ; In addition, the exposure limit of laser light reflected in the eye is Please refer to the fourteenth figure, where Q and .T 1 are the same as the twelfth figure.

The double pulse lighting of the present invention is exemplified by a white light band λ = 465 nm irradiation time of 1 second. Since the white light source is directly irradiated to the eye by 35 mm, it is classified according to the safety classification of the medical laser safety standard Z-13 6.1. Lighting, the energy density limit is available (2): Energy density limit = 1.8, / recognition (2)

=1 ·8χ 1/VT =1 . 8 m J / ( cm2 · sr ) Power density limit = energy density limit / time (3 ) = 1.8/1 =1 . 8m W / ( cm2 · sr) The laser light standard to regulate the LED light source with different dimming is obviously too strict. The general specification, the line width of white LED is 50nm, * the single mode laser light is 5 nm, so the power density of laser light is much larger than that of white LED. Power density, taking the line width specification as an example, the white LED is about 1 / 1 0 of the laser light, so we define the white light with the value of the first stage laser light power of z 1 3 6 · 1 LED optical power limit value to avoid eye 15 i

1285544 Eyes are affected by white light. According to the above calculation, the first-order laser light power density of λ = 465 nm is 1 · 8 m W / cm 2 , and the power density of the white light L E D is calculated to be 18 mW/cm 2 . We calculate the power output of the required white LED. We use YL5N3H2 series white LED, the specifications are as follows: luminescence wavelength 465 nm, optical output power 20mW, half power angle 15 product 5mm diameter packaging, working voltage Min: 3.2V, Typ. :3 M ax 3 · 6 V 〇 Suppose our white LEDs directly illuminate the eye at a distance of 5 degrees. And the solid angle Q=2; r(l-cosl5°) = 0· can get the power density on the surface of the eye ^ Ε = Φ cos 0 / d2 Ω = 20xcos5 〇 / (( 3 · 5 ) 2 x 0.2 1 4) = 7.6 m W/(cm2 · sr) Φ : Output power d : Distance between the LED and the eye: The value of the threshold is ,. , body .4V, 3 5 mm 214, (4)

0 : The angle between the chief ray of the LED and the normal line that is incident on the surface of the eye, so the calculated power density value of 7.6 m W / (cm2 · sr) is less than the limit of the power density value of 18mW / (cm2 · sr), indicating that the selected The LED (YL5N3H2 system, column) output power meets our safety limits. In summary, the advantages and effects of the present invention can be summarized as follows: [1] The imaging range is wider. The invention is a double-pulse light-receiving image, as long as the eye is located in the light-emitting range of the double-pulse light (whether the left and right sides of the double-pulse light eye or the upper and lower sides are the same), it falls into the white light system. In the circle "1285544" around the "line", the image capture range is wider than the previous single "point". [2] The image is more complete. In the invention, the two images after the double-pulse light-receiving image are combined into one, and the portion where each image is reflected by the light-removing point is removed, and the portion where the other image is not lighted is replaced, so A complete image of the iris, iris detection is more accurate.

[3] Safe lighting design. The invention adopts white light LED as the light source of double pulse lighting, and adopts the safety limitation of the medical laser system for the light standard related to human injury, and performs safety test on the optical power of white light to derive the white LED to the eye. Safety restrictions for safe and efficient lighting. [4] Ingestion of images is easy to record. The invention transmits the image of the eye to the analysis device through the network camera, and can take 40 images in about one second, which can clearly indicate the time of each image shooting and the time of the signal, and the process of the entire lighting process is easy. grasp. The present invention has been described in detail by the preferred embodiments of the present invention. From the above detailed description, those skilled in the art can understand that the present invention can achieve the foregoing objects, and the invention has been in compliance with the provisions of the patent law. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of a preferred embodiment of the present invention. FIG. 3 is a flow chart showing a fourth embodiment of a light source control circuit for controlling a pulse lighting system of the present invention. A and fourth B diagrams are diagrams showing the positions and internal structures of some of the components of the present invention.

5 is a schematic diagram of electrical connection of some components of the present invention. FIG. 6 is a schematic diagram showing the position and internal structure of some components of the present invention. FIG. 7 is a reference diagram of the adjustable power supply circuit of the present invention. Ninth and tenth views of the light source control circuit of the present invention are the reference diagrams of the pulse lighting and image capturing process of the present invention. FIG. 11 is a reference diagram of the pulse intensity and the preferred image capturing time of the present invention. Twelfth diagram is a diagram showing the relationship between the correction coefficient and the wavelength of the laser light according to the present invention. FIG. 14 is a diagram showing the exposure of the laser light to the eye. Quantity limit table [Main component symbol description] 1 0 image capture device 1 0 1 image capture lens 1 1 first image 1 1 1 first reflection point 1 2 second image 1 2 1 second reflection point 1 3 mask 20 light source Control circuit 18 1285544

2 1 serial transmission interface 22 voltage level conversion element 23 optical coupling element 24 adjustable power supply circuit 30 pulse lighting system 40 analysis device 50 object to be tested 60 complete image 91 computer 92 million order flow row first The predetermined time T2 is the second predetermined time PI1 - the upper discarding zone P 1 2 - the lower reserved zone PI 3 the first - merged zone P2 1 the second lower discarding zone P22 the second upper reserved zone P23 the second merged zone L Image path

19

Claims (1)

1285544 X. Patent application scope: 1 · A pulse-lighting iris image capturing and light source control system includes an image capturing device, a light source control circuit, a pulse lighting system and an analyzing device, wherein: the image capturing device Correlating with the lighting of the pulse lighting system at a first predetermined time and a second predetermined time, capturing a first image and a second image of an object to be tested, and in the first image and A first upper discarding zone and a second lower discarding zone are respectively generated on the second image; The light source control circuit controls the pulse lighting system to light the first predetermined time and the second predetermined time; the pulse lighting system performs trapezoidal pulse lighting on the object to be tested, and the first The second image respectively generates a first light reflecting point and a second light reflecting point, wherein the first light reflecting point and the second light reflecting point are respectively located on the first upper discarded area and the second lower abandoned area; the analyzing device, And extracting the iris regions of the first and second images respectively captured by the first predetermined time and the second predetermined time, respectively, respectively, the first and second images of the first and second images, and the first and second regions of the first and second images, and the second The lower scraping area is shaved, and then the two iris images after shaving the first upper discarding area and the second lower discarding area are combined by linear combination to complete the complete image of the iris. 2. The pulse-lighting iris image capturing and light source control system according to claim 1, wherein: the image capturing device is provided with at least one image taking lens, and the image capturing lens is in the first predetermined time And the second predetermined time, in conjunction with the pulse lighting 20 1285544 The illumination of the system is performed on the first image and the second image to be measured on a path of a traveling image, and a mask is arranged around the image capturing lens, and the mask is substantially surrounded by the Like the lens and the outside of the punching light system, to maintain the light effect of the pulse lighting system, the light source control circuit includes at least: a serial transmission interface f, which transmits the opening and number to the pulse lighting system, and then controls the pulse The light system is illuminating; a voltage level conversion component is electrically connected to the serial transmission section, and is used for converting the voltage transmission level of the serial transmission interface. The optical coupling component is operated by the light signal, completely Blocking the signal to avoid the reverse current interruption of the serial transmission interface. The adjustable power supply circuit includes at least two transistors, and the input voltage source is a 12V transformer, and the variable resistor is used to adjust the voltage. The pulse lighting system emits a moderate brightness. The pulse lighting system includes at least two white light-emitting diodes, and is respectively disposed on the upper and lower sides of the image taking device of the image capturing device. The measuring device is trapezoidal double-pulse lighting; the analyzing device uses the image segmentation technology to take out the first image and the second iris region respectively captured by the first pre-interval and the second predetermined time, and take out the iris region in the iris region. After that, the octagonal regions of the medical points are separately segmented; that is, the first upper discarded area, the first reserved area, and the plurality of first merged areas are respectively formed on the first image, and are divided into the second image on the second image. The discarding area, a second upper reserved area, and a plurality of first object images have a pulse rate; the closed interface, the current and the borrowing to adjust the 9-pole body, and the timing image is in the middle and the second shape 21 1285544; retaining the first lower reserved area of the first image and the second image retaining area, discarding the first upper discarding area of the first image and the second lower discarding area of the first image; and then the first and second images First, the parallel combination is linearly formed to form a complete image for detecting the iris. 3. The pulse-lighting iris source light source control system described in the second claim of the patent application, wherein: the image capturing device is a a webcam; the object to be tested is an eye; the serial transmission interface is disposed on a human computer; 1' the voltage level conversion component is used to press the serial transmission interface level to - 12V~12V is converted into 0V~5V; the first predetermined time is about an intermediate period when the upper LED pulse light is the brightest and the brightness is reduced, and the first image is taken by the head; The predetermined time is about the same as the pulse light of the upper LED and the brightness of the pulse of the lower LED is the same as that of the upper two-pulse light, and the eye size of the subject is the same as the first image. Second image The first upper discarding zone of the first image is located at an angle of 67·1 to 1 1 2 · 5 degrees; the second lower discarding zone of the second image is located between an angle of 2 4 7 · to 292.5 degrees; The merger is an interpolation method. The second image and the second image of the image and the appearance of the image appear in the polar body about 5 degrees 5 degrees 22 1285544 4 - The pulse-lighting iris image capturing and light source control system according to the second aspect of the invention, wherein the two white light-emitting diodes of the pulse lighting system can also be disposed in the image capturing device Take the left and right sides of the lens. 5) The pulse-lighting iris image capturing and light source control system according to claim 1, wherein: the image capturing device is electrically connected to a computer by a 10,000-stage flow row, and the computer is coupled to the light source The control circuit and the analysis device are electrically connected; the image of the subject's eyes is transmitted to the analysis device, and the number of shots to be taken, the number of seconds to be taken, and the time and signal time and time of each image can be marked. Mode; the pulse illuminating system performs safe double pulse illuminating on the object to be tested at a first predetermined time and a second predetermined time interval of about 1 〇 milliseconds, and the double pulsed light corresponds to the eye of the subject The first upper discarding zone and the second lower discarding zone are approximately trapezoidal; the linear combination means that when the upper half of the first and second images are close, the weight of the upper half is relatively large, and when the lower half is close, the lower half is The weight of the part is relatively large, and the results of the first and second images are obtained by linear interpolation. twenty three