Tuesday, August 17, 2021

Color-Coding the Pandemic


Michael H. Brill, Datacolor

(Send contributions to mbrill@datacolor.com )

Each of us has a different life story through the pandemic. My story does not include the uneasy “new normal” experienced by students in school. Part of the “new normal” requires students to attend school in staggered part-time schedules. How did kids react to this complication? In curiosity, I Googled my old high-school newspaper, the Brentwood Pow Wow. (Yes, the Native American name remains.) Immediately a web page appeared with an article for their April Fools’ edition: “Satire: Crayola Box Plan to Replace Original Tri-color Hybrid Plan;” author, Lilian Velasquez; dateline, 24 March 2021. This was going to be about color coding, about the resilience of young people, and maybe more.

The school had seen fit to illuminate the monthly calendar with color-coded parts to clarify three alternative student schedules. That was the original Tri-color plan. Ms. Velasquez started with a calendar illustrating the Tri-color plan (using the first three entries on the list below), and then “sprinkled in” the rest:

Teal: Fully remote students  
Gold: Hybrid students attend school on Tuesday and Fridays, and alternating Wednesdays.
Green: Hybrid students attend school on Monday, Thursday, and alternating Wednesdays.
Chocolate: Attend school 9 times a year, on the first Monday of each month.
Cherry: Attend school every day for only 4 hours each day from 9 a.m. to 1 p.m.
Magenta: Attend school only on Fridays for 16 hours.
Indigo: Attend school on the weekends from 7 a.m. to 2 p.m. (Saturday and Sunday)
Silver: Attend school twice a month on the 7th and on the 21st.

Velasquez then showed a typical one-month calendar annotated with a delightfully confusing panoply of font colors: a scheme that might give new meaning to the term “drop-out colors.” It’s the kind of gentle extrapolation one expects from high-school students in an April Fools’ satire. I remember reading such extrapolations and writing them. The genre was grounded in acceptance of the normal. Now it is the “new normal.”

Before I went to Russia in 2008 to teach English as a Second Language (ESL), I heard that Russians would characteristically respond to a story of complaint and indignation by declaring, “It is normal.” My trip confirmed that assertion. I think that every time we reset the condition that we consider normal, we rewrite the past to conform. It is a coping mechanism, and it is helped along by writers.

In the same vein, Jorge Luis Borges said: “Every writer ‘creates’ his own precursors. His work modifies our conception of the past, as it will modify the future.” The better the writer, the more responsibility this incurs.

Still, the past is not easily erased. Brentwood High School retains Native American metaphors. Our media preserve other metaphors, as does our collective memory—sometimes unconsciously. Borges himself, with his quote, immortalizes his own present (and our recent past) by using “his” instead of “their” in describing a hypothetical writer.

It is a delicately balanced narrative into which Ms. Velasquez entered as she wrote extrapolating a color code for the “new normal.” She writes well, and her underlying optimism can encourage us all. I wish her the best as she extrapolates further—we hope from a better “new normal.”

And perhaps her new color code foretells a career as an artist or color scientist!

Michael H. Brill
BHS Class of 1965

Monday, May 10, 2021

Into Something Rich and Strange


About 30 years ago [1] I encountered aerial photographs that were captivating, rich and strange. The photographs were acquired with a camera geometry similar to that of a flash-attached pinhole camera. The light flashed, reflected off the surface of the Earth, and then returned to the camera, all via straight-line paths. But such an image didn’t look at all like it came from a pinhole camera. Most of the spatial features were familiar, but long black shadows appeared between them. We don’t usually see cast shadows in flash-attached-camera images, because any object producing such a shadow hides it from sight. That’s why the contrasts are so low and unappealing in photographs from an old-style flash camera. But the new image broke that rule, exhibiting shadows as if they were cast by a setting sun in the evening: a romantic image, as it were.


What were these strange cameras? To answer the “what” question, I must first answer “why,” and that will break the romantic thrall. In the last century, interest in viewing the Earth from space was beset by the problem that most of the Earth is having a cloudy day just now (for any now). To see through the clouds, you need to use light with long wavelengths. Microwaves worked, and they became the basis of imaging radar systems.


Could you make a pinhole camera system with a microwave light source? No—you couldn’t focus the beam or tell where it was coming from when it returned. The designers of this camera had to give up on the conventional idea of capturing on a flat film the direction of a viewed object on the Earth (called a world point). Instead, they did a clever thing. They flashed a complicated microwave pulse (called a chirp) in all directions, and then captured reflected returns. They sorted the light-intensity returns according to their time delay from the source (proportional to the range of the world point) and also according to their time scaling (proportional to Doppler effect). Oh yes, I must mention that the new camera had to be moving relative to the Earth, and its velocity had to be known, whereupon this second piece of information became proportional to the cosine of the angle from the vehicle direction and that of the world point. If you know the range of a world point, then that locates it on a sphere centered on the camera. If you know the vehicle direction, then you know the angle between the velocity and the direction to the world point, and that places the world point on a cone with its vertex at the camera. Knowing the world point’s range sphere and Doppler cone means that you have identified a circle in space on which the world point must lie. Such circles are called projection circles.


Now let’s return to a comparison of our new camera with a pinhole camera. If you look at a world point along a line of sight through a pinhole camera, you can tell what line the world point is on (identified by direction), but you can’t tell how far along the line the world point resides. If you look at a world point for the new camera, you know which projection circle the world point is on, but you can’t tell which point on the circle is occupied by the world point. Somehow in this imaging system, even though the light still travels in straight lines, the part of the 3D world point location that is inaccessible on a 2D image is a circle and not one of those straight lines. The romantic thrall has ended, but for me the mathematical thrall has begun!


The new camera, by the way, is called a synthetic-aperture-radar (SAR) system [2]. And that brings me to another comparison with a conventional camera. Instead of ending up in a light-sensitive medium such as film, the SAR’s rays enter a localized receiver and are mathematically sorted to provide the coordinate locations (range and Doppler) in a mathematically defined structure called a synthetic aperture. That plane does not correspond to a physical object, but is a mathematical structure in 3D. It’s not so strange, really. That kind of structure is common in holography, hence the term “quasi-holographic” that is used to describe the SAR technology.


Of course, you will need to know how the conventional and new cameras work together to reconstruct the three dimensions of a world point. The answer is: quite well. It is common [3] to solve for a 3D point using a camera image and a SAR image (see Fig. 1). The process is similar to triangulation as used by pairs of conventional cameras.


Now some of you may wonder where the shadows enter all of this. The straight-line light propagation certainly leaves cast shadows, but these shadows occupy noticeable area in a SAR image (e.g., search SAR image example). The pixels there are dark because no light intensity is directed to them by the math algorithm. The SAR shadows are called layover. It’s ho-hum and official. Yet somehow, I sense we are “into something rich and strange,” to offer an Ariel perspective.


This brings me to my final point. I don’t believe artists have yet explored SAR technology as a medium for expression. So, following the lead of Anish Kapoor as described by Carl Jennings’s essay in this issue, I hereby deny anybody but me the right to use SAR in art. So there, IP attorneys!


Note: This essay is dedicated to Dr. Eamon B. Barrett, my long-time friend and collaborator in imaging mathematics, who passed away March 30 after a long illness. MHB



[1] Brill M, Triangulating from optical and SAR images using direct linear transformations, Photogram. Eng. & Rem. Sensing 53 (1987), 1097-1102.

[2] Ausherman, DA, et al., Developments in radar imaging, IEEE Trans. Aerospace & Electronic Sys. AES-20 (1984), 363-400.

[3] Qiu C, Schmitt M, Ziu X, Towards automatic SAR-optical stereogrammetry over urban areas using very high resolution imagery. ISPRS J Photogram & Remote Sens 138 (2018), 218-231.


Michael H. Brill




Fig. 1. Triangulation of a world point X as the intersection of camera line-of-sight L and SAR projection circle C. The quantity w2 is the velocity of the SAR sensor, and image points Y1 and Y2 are camera and SAR images of X. [adopted from Ref. 1]