15-862 Computational Photography
|Project 0: The Vertigo Shot - by Frank Palermo|
The images used in this project were captured with a Canon PowerShot G9 digital camera. This particular camera is equipped with an image sensor 7.6mm wide and a lens with adjustable focal lengths from 7.4mm to 44.4mm. The lens focal length (among other camera functions) may be remotely controlled via USB using a third-party software utility. When this utility is employed, it becomes possible to set the lens focal length to any one of 14 individual positions. These positions, along with their corresponding horizontal angle of view (calculated using the formula 2 arctan(7.6 / (2f)) ), are listed in the table below:
In order to replicate the effect of the "Vertigo Shot," the camera was first set to the minimum zoom (7.4mm) and positioned near the subject. Without altering the zoom, the camera was moved closer to or further from the subject until the desired composition for the initial frame was obtained. The resulting distance "d" from the subject was then used (along with the angle of view table above) to calculate the width of the camera's field of view in the plane of the subject (i.e. w = 2d tan(54.36°/2) ). Finally, the reverse of this calculation (i.e. d = w / (2 tan(angle/2)) was used to find the distance required to match this width at each zoom level. By moving the camera to the calculated distance away from the subject at each zoom level, the subject's appearance was kept mostly unchanged while the appearance of background and foreground objects changed drastically (i.e. the "Vertigo" effect).
Careful control of the lens focal length and camera position allowed for reasonably "smooth" transitions between frames of the captured sequence. To compensate for the remaining imprecision in these parameters, the images were carefully aligned before assembly into the final animations. Additionally, any images which were particularly misaligned from the others were omitted from the sequence (fortunately, each sequence produced at least 9 usable frames out of the 14 captured). In some cases, the decision was made to reverse the order of the frames (thereby reversing the motion of the effect) for aesthetic purposes.
The completed "Vertigo Shot" sequences are reproduced below. Each image has been cropped to 640x480 for web publication (resized to 320x240 when displayed on this page).
Sequence #1: Window
In this example, the subject (a window frame) was chosen to be relatively flat. Therefore, we see very little change in the subject as the distant background becomes increasingly magnified.
Sequence #2: Train (Moving Camera)
In this example, the subject (a toy train) was chosen to have significant depth extending away from the camera. Additionally, a miniature tree was placed into the scene at a different distance away from the camera. Therefore, we see differing motion of each of the three elements (the train, the tree, and the backdrop), in addition to the appearance of stretching and lengthening of the train as the perspective changes.
"Bells & Whistles" #1 - Moving Subject
The toy train in Sequence #2 perfectly lends itself to an attempt of moving the subject of the photographs rather than the camera. (The distance calculations and general procedure used were similar to the two sequences above).
"Bells & Whistles" #2 - Field of View
As described in the "Introduction" section above, field-of-view and angle-of-view calculations were done across the entire zoom range in order to position the camera for optimum effect.
"Bells & Whistles" #3 - Animated GIFs
In order to more clearly see the "Vertigo" effect at work, the three sequences captured were assembled into Animated GIFs using Adobe Photoshop CS3. Each frame is displayed for 0.1s, and the animations have been resized to 320x240 in order to conserve space.
Conclusion (Difficulties Encountered)
The most notable difficulty encountered with this project was with establishing "smooth" transitions between successive frames; this was especially true near the extreme ends of the 7.4mm-44.4mm focal length range. As noted above, these problems were addressed chiefly by positioning the camera as carefully as possible and carefully aligning the resulting pictures before the animations were assembled.