June 3, 2004

Contents

### Measurement of Length and Angle

Image has tools for measuring length and angle. This exercise demonstrates a visual illusion by measuring lengths on a digital image of the Gateway Arch in St Louis, Missouri. We will also measure angles.

• File -> Open menu, select the Sample Images / Illusions / Gateway arch.tiff image. (For printing this example, I've reduced the size of the image by a factor of two using the Edit -> Scale & Rotate Image / Scale menu. )

The outer width of the arch, measured at the base, is equal to the height, although it may not look like it. To measure the distances

• Select either the
• line selection tool: ()(which does not alter the image), or the
• (Does not apply to ImageJ) profile tool (which draws a line using the color of the brush tool which is a medium gray here. (ImageJ - Analyze / Plot Profile will plot a profile along the line selection tool.)
• (I use the line selection tool here).
• (Not applicable to ImageJ). Make sure the Info window is visible (not overlapping the image) because the length information does not 'stick around'.
• Make a selection line across the base of the arch
• (Immediately after clicking on the line selection tool:)
• Move the mouse to, say, the left side
• Click and hold down the mouse button
• Drag over to the right side of the arch (see selection line in figure below:)
•  Image ImageJ
• Read and memorize the length (On the full sized image, it is 1.26 in (502.08). The number in parentheses is the length in pixels. The units of the first length are set by the Analyze -> Set Scale menu. I usually use pixels.
• When you let up on move the mouse button, the length will disappear from the status barYou can redisplay the length by selecting one of the three handles of the selection line and moving it slightly.  Moving the center one will not change the length.
• Make a similar selection for the (outer) height of the arch, reading the length. (496 pixels).

• ### Angle Measurement

• To measure the angle of elevation of the inside of the arch at the base:
• Click on the angle tool .
• Make sure the Info window status bar of the ImageJ window is visible, when measuring lengths.
• To measure the angle from the horizontal axis of the window:
• Click (no need to hold) the mouse on point B A.
• Note that the angle changes as the mouse is moved around.
• With the mouse on point A B, the angle is close to 0 deg. Click on point A B.
• With the mouse on point C, the angle is ~83 deg. Click on point C to "freeze" the tool.
• The reading after the mouse click is not used. It is the angle between the dotted lines.
• (Click again to immediately initiate another angle reading.)
• To measure an arbitrary angle (the inside angle at the base of the arch, in the photograph)
• Click on point A.
• Click on point B, making a 'rubber band line' between the two points.
• Move the mouse to point C, noting the angle of about 82.3 deg.