Walrus tusk?

they look like bison horn cores to me.

What is the collecting data?

The quality of these images is poor. Here are some suggestions for improving them, thus improving your chances of getting confirmation of your ID.

LIGHT IT UP. Use as much ambient light as possible to reduce shadows. Halogen bulbs are better for photography than tungsten filament bulbs. The new compact flourescent bulbs come in a "daylight" (6500K) version that you can use in any (non-dimming) fixture and produce very little heat.

BRIGHTEN AND CONTRAST. BRIGHTEN the image until the fossil appears slightly washed, then adjust the CONTRAST until the fossil is bright and sharp and is a good color-match. Practice this until you get a feel for it.

CROP, CROP, CROP. Again, use the image-editing software to crop the image to only what is pertinent. Leave only a narrow margin around the fossil. The more of your kitchen counter-top in the image, the smaller the fossil image will be.